This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 θ 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 θ AB = vector A · vector B bardbl vector A bardblbardbl vector B bardbl = − 23 . 2 (6 . 49384) (8 . 59593) = − . 415617 θ 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 ˆ (with A > 0), armington (kma786) – hw0203 – fiete – (57165) 2 vector B = − B ˆ ı (with B > 0), and therefore...
View
Full Document
 Spring '07
 Swinney
 mechanics, Dot Product, 2k, 3 k, Righthand rule

Click to edit the document details