ict02 - Version 017/AABAB ict 02 Turner(92510 Ax = 2.4 A y...

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Version 017/AABAB – ict 02 – Turner – (92510) 1 This print-out should have 2 questions. Multiple-choice 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 = 2 . 4 , A y = 5 , A z = 1 . 6 , while vector vector B has components B x = 6 . 7 , B y = 3 . 2 , B z = 4 . 1 . What is the angle θ AB between these vec- tors? (Answer between 0 and 180 .) 1. 121.416 2. 156.52 3. 111.897 4. 132.968 5. 89.7192 6. 97.2163 7. 115.127 8. 84.0386 9. 93.1496 10. 137.806 Correct answer: 121 . 416 . Explanation: bardbl vector A bardbl = radicalBig A 2 x + A 2 y + A 2 z = radicalBig ( 2 . 4) 2 + 5 2 + 1 . 6 2 = 5 . 77235 and bardbl vector B bardbl = radicalBig B 2 x + B 2 y + B 2 z = radicalBig 6 . 7 2 + ( 3 . 2) 2 + 4 . 1 2 = 8 . 48175 , so using vector A · vector B = A x B x + A y B y + A z B z = ( 2 . 4) 6 . 7 + 5 ( 3 . 2) + 1 . 6 (4 . 1) = 25 . 52 , cos θ AB = vector A · vector B bardbl vector A bardbl bardbl vector B bardbl = 25 . 52 (5 . 77235) (8 . 48175) = 0 . 521246 θ AB = arccos( 0 . 521246) = 121 . 416 . Two vectors can define a plane. When these two vectors are plotted in this plane, we have A B 121 . 416 002 10.0 points Two airplanes leave an airport at the same time. The velocity of the first airplane is 680 m / h at a heading of 57 . 7 . The velocity
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