{"id":2345,"date":"2020-10-30T07:44:00","date_gmt":"2020-10-30T07:44:00","guid":{"rendered":"http:\/\/onlineclassesguru.com\/?p=2345"},"modified":"2020-10-30T07:44:00","modified_gmt":"2020-10-30T07:44:00","slug":"determining-the-components-of-a-vector","status":"publish","type":"post","link":"https:\/\/onlineclassesguru.com\/index.php\/2020\/10\/30\/determining-the-components-of-a-vector\/","title":{"rendered":"Determining the components of a vector"},"content":{"rendered":"<style type=\"text\/css\"><\/style><p>Tactics Box 3.3 Determining the Components of a Vector<\/p>\n<p>Learning Goal:<\/p>\n<p>To practice Tactics Box 3.3 Determining the component of a vector.<\/p>\n<p>When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This Tactics Box describes how to determine the x component and y component of vector , denoted and .<\/p>\n<p>TACTICS BOX 3.3 Determining the components of a vector<\/p>\n<p>1. The absolute value of the x component is the magnitude of the component vector .<\/p>\n<p>2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction.<\/p>\n<p>3. The y component is determined similarly.<\/p>\n<p>Part A<\/p>\n<p>What is the magnitude of the component vector shown in the figure?<\/p>\n<p>Express your answer in meters to two significant figures.<\/p>\n<p>ANSWER:<\/p>\n<p>Part B<\/p>\n<p>What is the sign of the y component of vector shown in the figure?<\/p>\n<p>A \u20d7 A \u20d7 x A \u20d7 y<\/p>\n<p>A \u20d7 Ax Ay<\/p>\n<p>| |Ax Ax A \u20d7 x<\/p>\n<p>Ax A \u20d7 x A<\/p>\n<p>\u20d7 x<\/p>\n<p>Ay<\/p>\n<p>A \u20d7 x<\/p>\n<p>= | |Ax m<\/p>\n<p>Ay A \u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 2\/21<\/p>\n<p>ANSWER:<\/p>\n<p>Part C<\/p>\n<p>This question will be shown after you complete previous question(s).<\/p>\n<p>Components of Vectors<\/p>\n<p>Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified.<\/p>\n<p>Part A<\/p>\n<p>What is the x component of ?<\/p>\n<p>Express your answer to two significant figures.<\/p>\n<p>positive negative<\/p>\n<p>A \u20d7 D\u20d7<\/p>\n<p>A \u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 3\/21<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>Part B<\/p>\n<p>What is the y component of ?<\/p>\n<p>Express your answer to the nearest integer.<\/p>\n<p>ANSWER:<\/p>\n<p>Part C<\/p>\n<p>What is the y component of ?<\/p>\n<p>Express your answer to the nearest integer.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>Part D<\/p>\n<p>What is the component of ?<\/p>\n<p>Express your answer to the nearest integer.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation.<\/p>\n<p>The answers below are all integers, so estimate the components to the nearest whole number.<\/p>\n<p>= Ax<\/p>\n<p>A \u20d7<\/p>\n<p>= Ay<\/p>\n<p>B\u20d7<\/p>\n<p>= By<\/p>\n<p>x C \u20d7<\/p>\n<p>= Cx<\/p>\n<p>A \u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 4\/21<\/p>\n<p>Part E<\/p>\n<p>In ordered pair notation, write down the components of vector .<\/p>\n<p>Express your answers to the nearest integer.<\/p>\n<p>ANSWER:<\/p>\n<p>Part F<\/p>\n<p>In ordered pair notation, write down the components of vector .<\/p>\n<p>Express your answers to the nearest integer.<\/p>\n<p>ANSWER:<\/p>\n<p>Part G<\/p>\n<p>What is true about and ? Choose from the pulldown list below.<\/p>\n<p>ANSWER:<\/p>\n<p>Problem 3.15<\/p>\n<p>A wildlife researcher is tracking a flock of geese. The geese fly 4.5 due west, then turn toward the north by 50 and fly another 5.0 .<\/p>\n<p>Part A<\/p>\n<p>How far west are they of their initial position?<\/p>\n<p>Express your answer to two significant figures and include the appropriate units.<\/p>\n<p>ANSWER:<\/p>\n<p>Part B<\/p>\n<p>B\u20d7<\/p>\n<p>, = Bx By<\/p>\n<p>D\u20d7<\/p>\n<p>, = Dx Dy<\/p>\n<p>B\u20d7 D\u20d7<\/p>\n<p>They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors.<\/p>\n<p>km \u2218 km<\/p>\n<p>= dw<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 5\/21<\/p>\n<p>What is the magnitude of their displacement?<\/p>\n<p>Express your answer to two significant figures and include the appropriate units.<\/p>\n<p>ANSWER:<\/p>\n<p>Problem 3.5<\/p>\n<p>A position vector with magnitude 20 points to the right and up. Its -component is 16 .<\/p>\n<p>Part A<\/p>\n<p>What is the value of its -component?<\/p>\n<p>Express your answer to two significant figures and include the appropriate units.<\/p>\n<p>ANSWER:<\/p>\n<p>Problem 3.2<\/p>\n<p>Part A<\/p>\n<p>Draw the vector .<\/p>\n<p>ANSWER:<\/p>\n<p>= d<\/p>\n<p>m x m<\/p>\n<p>y<\/p>\n<p>= y<\/p>\n<p>= +C \u20d7 A \u20d7 B\u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 6\/21<\/p>\n<p>Part B<\/p>\n<p>Draw the vector .<\/p>\n<p>ANSWER:<\/p>\n<p>= \u2212D\u20d7 A \u20d7 B\u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 7\/21<\/p>\n<p>Problem 3.1<\/p>\n<p>Part A<\/p>\n<p>Draw the vector .<\/p>\n<p>ANSWER:<\/p>\n<p>Part B<\/p>\n<p>Draw the vector .<\/p>\n<p>ANSWER:<\/p>\n<p>= +D\u20d7 A \u20d7 B\u20d7<\/p>\n<p>= \u2212C \u20d7 A \u20d7 B\u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 8\/21<\/p>\n<p>Vector Magnitude and Direction Conceptual Question<\/p>\n<p>A man out walking his dog makes one complete pass around a perfectly square city block. He starts at point A and walks clockwise around the block.<\/p>\n<p>Let be the displacement vector from A to B, be the displacement vector from B to C, etc.<\/p>\n<p>Part A<\/p>\n<p>Which of the following vectors is equal to ?<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>r \u20d7 AB r \u20d7 BC<\/p>\n<p>r \u20d7 AB<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 9\/21<\/p>\n<p>ANSWER:<\/p>\n<p>Part B<\/p>\n<p>Which of the following vectors is equal to ?<\/p>\n<p>ANSWER:<\/p>\n<p>Part C<\/p>\n<p>Which of the following vectors is equal to ?<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>Adding and Subtracting Vectors Conceptual Question<\/p>\n<p>Six vectors (A to F) have the magnitudes and directions indicated in the figure.<\/p>\n<p>only<\/p>\n<p>only<\/p>\n<p>only All of the above None of the above<\/p>\n<p>r \u20d7 BC r \u20d7 CD r \u20d7 DA<\/p>\n<p>\u2212r \u20d7 AB<\/p>\n<p>only<\/p>\n<p>only<\/p>\n<p>only All of the above None of the above<\/p>\n<p>r \u20d7 BC r \u20d7 CD r \u20d7 DA<\/p>\n<p>\u2212r \u20d7 AB r \u20d7 DA<\/p>\n<p>only<\/p>\n<p>only<\/p>\n<p>only All of the above None of the above<\/p>\n<p>\u2212( + )r \u20d7 CD r \u20d7 DA +r \u20d7 AB r \u20d7 BC \u2212r \u20d7 BC r \u20d7 CD<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 10\/21<\/p>\n<p>Part A<\/p>\n<p>Which two vectors, when added, will have the largest (positive) x component?<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>Part B<\/p>\n<p>Which two vectors, when added, will have the largest (positive) y component?<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>Part C<\/p>\n<p>C and E E and F A and F C and D B and D<\/p>\n<p>C and D A and F E and F A and B E and D<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 11\/21<\/p>\n<p>Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude?<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>Vector Addition Ranking Task<\/p>\n<p>Six vectors ( through ) have the magnitudes and directions indicated in the figure.<\/p>\n<p>Part A<\/p>\n<p>Rank the vector combinations on the basis of their magnitude.<\/p>\n<p>Rank from largest to smallest. To rank items as equivalent, overlap them.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>A and F A and E D and B C and D E and F<\/p>\n<p>a \u20d7 f \u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 12\/21<\/p>\n<p>Part B<\/p>\n<p>Rank the vector combinations on the basis of their angle, measured counterclockwise from the positive x axis. Vectors parallel to the positive x axis have an angle of 0 . All angle measures fall between 0 and 360 .<\/p>\n<p>Rank from largest to smallest. To rank items as equivalent, overlap them.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>\u2218 \u2218 \u2218<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 13\/21<\/p>\n<p>Adding Scalar Multiples of Vectors Graphically<\/p>\n<p>Draw the vectors indicated. You may use any extra (unlabeled) vectors that are helpful; but, keep in mind that the unlabeled vectors should be deleted before submitting your answer.<\/p>\n<p>Part A<\/p>\n<p>Draw the vector .<\/p>\n<p>The length and orientation of the vector will be graded. The location of the vector is not important.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>= + 2C \u20d7 A \u20d7 B\u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 14\/21<\/p>\n<p>Part B<\/p>\n<p>Draw the vector .<\/p>\n<p>The length and orientation of the vector will be graded. The location of the vector is not important.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>= 1.5 \u2212 3C \u20d7 A \u20d7 B\u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 15\/21<\/p>\n<p>Part C<\/p>\n<p>Draw the vector .<\/p>\n<p>The length and orientation of the vector will be graded. The location of the vector is not important.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>= 0.5 + 2C \u20d7 A \u20d7 B\u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 16\/21<\/p>\n<p>Tactics Box 3.1 Subtracting Vectors<\/p>\n<p>Learning Goal:<\/p>\n<p>To practice Tactics Box 3.1 Subtracting vectors<\/p>\n<p>Vector subtraction has some similarities to the subtraction of two scalar quantities. With numbers, subtraction is the same as the addition of a negative number. For example, is the same as . Similarly,<\/p>\n<p>. We can use the rules for vector addition and the fact that is a vector opposite in direction to to form rules for vector subtraction, as explained in this Tactics Box.<\/p>\n<p>TACTICS BOX 3.1 Subtracting vectors<\/p>\n<p>To subtract from perform these steps:<\/p>\n<p>1. Draw .<\/p>\n<p>2. Place the tail of at the tip of .<\/p>\n<p>5 \u2212 3 5 + (\u22123) \u2212 = + (\u2212 )A \u20d7 B\u20d7 A \u20d7 B\u20d7 \u2212B\u20d7<\/p>\n<p>B\u20d7<\/p>\n<p>B\u20d7 A \u20d7<\/p>\n<p>A \u20d7<\/p>\n<p>\u2212B\u20d7 A \u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 17\/21<\/p>\n<p>3. Draw an arrow from the tail of to the tip of . This is vector .<\/p>\n<p>Part A<\/p>\n<p>Find vector by following the steps in the Tactics Box above. Make certain to draw with the correct orientation.<\/p>\n<p>ANSWER:<\/p>\n<p>Part B<\/p>\n<p>Find vector by following the steps in the Tactics Box above. Make certain to draw with the correct orientation.<\/p>\n<p>ANSWER:<\/p>\n<p>A \u20d7 \u2212B\u20d7 \u2212A \u20d7 B\u20d7<\/p>\n<p>= \u2212C \u20d7 A \u20d7 B\u20d7 \u2212B\u20d7<\/p>\n<p>= \u2212F \u20d7 D\u20d7 E \u20d7 \u2212E \u20d7<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 18\/21<\/p>\n<p>\u00b1 Resolving Vector Components with Trigonometry<\/p>\n<p>Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system.<\/p>\n<p>Part A<\/p>\n<p>Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown.<\/p>\n<p>Enter the x component followed by the y component, separated by a comma.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>T \u20d7 T \u2218<\/p>\n<p>A \u20d7 a \u03b1 \u2218<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 19\/21<\/p>\n<p>ANSWER:<\/p>\n<p>Part B<\/p>\n<p>Find the components of the vector with length = 1.00 and angle =20.0 with respect to the x axis as shown.<\/p>\n<p>Enter the x component followed by the y component, separated by a comma.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>Part C<\/p>\n<p>Find the components of the vector with length = 1.00 and angle 35.0 as shown.<\/p>\n<p>Enter the x component followed by the y component, separated by a comma.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>\u00b1 Biking Vectors<\/p>\n<p>A student bikes to school by traveling first = 1.00 north, then = 0.500 west, and finally = 0.100 south.<\/p>\n<p>Part A<\/p>\n<p>If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance would the bird cover?<\/p>\n<p>Express your answer in miles.<\/p>\n<p>You did not open hints for this part.<\/p>\n<p>ANSWER:<\/p>\n<p>= A \u20d7<\/p>\n<p>B\u20d7 b \u03b2 \u2218<\/p>\n<p>= B\u20d7<\/p>\n<p>C \u20d7 c \u03d5 = \u2218<\/p>\n<p>= C \u20d7<\/p>\n<p>dN miles dW miles dS miles<\/p>\n<p>db<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 20\/21<\/p>\n<p>Part B<\/p>\n<p>This question will be shown after you complete previous question(s).<\/p>\n<p>Part C<\/p>\n<p>This question will be shown after you complete previous question(s).<\/p>\n<p>Part D<\/p>\n<p>This question will be shown after you complete previous question(s).<\/p>\n<p>Part E<\/p>\n<p>This question will be shown after you complete previous question(s).<\/p>\n<p>Part F<\/p>\n<p>This question will be shown after you complete previous question(s).<\/p>\n<p>Problem 3.8<\/p>\n<p>Josh is climbing up a steep 32 slope, moving at a steady 0.90 along the ground in .<\/p>\n<p>= db miles<\/p>\n<p>\u2218 m\/s<\/p>\n<p>10\/6\/2014 HW3<\/p>\n<p>http:\/\/session.masteringphysics.com\/myct\/assignmentPrintView?assignmentID=3212823 21\/21<\/p>\n<p>Part A<\/p>\n<p>How many meters of elevation does he gain in one minute of this climb?<\/p>\n<p>Express your answer to two significant figures and include the appropriate units.<\/p>\n<p>ANSWER:<\/p>\n<p><center><a href=\"http:\/\/onlineclassesguru.com\/orders\/ordernow\"><img decoding=\"async\" src=\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcTyj99p60XCLyLk1htB7-1neRt8-2QdnenNlQ&usqp=CAU\"target=\"_http:\/\/onlineclassesguru.com\/orders\/ordernow\"\/><\/center><p>","protected":false},"excerpt":{"rendered":"<p>Tactics Box 3.3 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.3 Determining the component of a vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This Tactics Box describes&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2345","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Determining the components of a vector - onlineclassesguru<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/onlineclassesguru.com\/index.php\/2020\/10\/30\/determining-the-components-of-a-vector\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Determining the components of a vector - onlineclassesguru\" \/>\n<meta property=\"og:description\" content=\"Tactics Box 3.3 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.3 Determining the component of a vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. 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