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Unformatted text preview: armington (kma786) hw0203 fiete (57165) 1 This printout should have 12 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Vector vector A has components A x = 1 . 4 , A y = 5 , A z = 3 . 9 , while vector vector B has components B x = 4 . 3 , B y = 6 . 4 , B z = 3 . 8 . What is the angle AB between these vec tors? (Answer between 0 and 180 .) Correct answer: 114 . 558 . Explanation: bardbl vector A bardbl = radicalBig A 2 x + A 2 y + A 2 z = radicalBig ( 1 . 4) 2 + 5 2 + 3 . 9 2 = 6 . 49384 and bardbl vector B bardbl = radicalBig B 2 x + B 2 y + B 2 z = radicalBig 4 . 3 2 + ( 6 . 4) 2 + 3 . 8 2 = 8 . 59593 , so using vector A vector B = A x B x + A y B y + A z B z = ( 1 . 4) 4 . 3 + 5 ( 6 . 4) + 3 . 9(3 . 8) = 23 . 2 , cos AB = vector A vector B bardbl vector A bardblbardbl vector B bardbl = 23 . 2 (6 . 49384) (8 . 59593) = . 415617 AB = arccos( . 415617) = 114 . 558 . Two vectors can define a plane. When these two vectors are plotted in this plane, we have A B 1 1 4 . 5 5 8 002 (part 1 of 2) 10.0 points Vector vector A points South. Vector vector B points West. What is the direction of their cross product vector A vector B ? 1. North 2. West 3. South 4. Vertically down correct 5. Vertically up 6. Southwest 7. vector A vector B a scalar and has no direction. 8. East 9. None of these 10. vector A vector B = vector 0; its direction is undefined Explanation: Apply the Right Hand Rule: Let your right thumb follow vector A and point South while the other four fingers follow vector B and point West. Your palm faces down; the direction of the cross product vector A vector B . Alternatively, using standard map direc tions, we have x axis pointingEast, the y axis pointing North and the z axis pointing Up. Consequently, vector A = A (with A > 0), armington (kma786) hw0203 fiete (57165) 2 vector B = B (with B > 0), and therefore...
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This note was uploaded on 02/11/2011 for the course PHY 301 taught by Professor Swinney during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Swinney
 mechanics

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