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Recitation Worksheet B Solutions

# Recitation Worksheet B Solutions - Worksheet B Vectors 1...

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Worksheet B: Vectors. 1. Let A = 2.0 i + 5.0 j 1.0 k = (2.0, 5.0, 1.0) B = 1.0 i + α j + 3.0 k = ( 1.0, α , 3.0) (Both notations will be used throughout the course). a. Find the magnitude of A . ( ) ( ) ( ) 2 2 2 2.0 5.0 1.0 5.5 = + + − = A b. Find α so that A and B are perpendicular to each other. This means that 0. (2.0)( 1.0) (5.0) ( 1.0)(3.0) 5.0 5.0 5.0 5.0 0 1.0 α α α α = = + + − = − + + = = G G G G A B A B c. Find the angle between A and B when α = 2.0. ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 2 2 2 2 2 1 cos (2.0)( 1.0) (5.0)( 2.0) ( 1.0)(3.0) cos 2.0 5.0 1.0 1.0 2.0 3.0 cos ( 0.732) 137 θ = + + − = + + − + − + = = ° G G A B AB d. Write the components of Â , the unit vector in the direction of A . ( ) (2.0,5.0, 1.0) 0.37,0.91, 0.18 5.5 5.5 (see part a) = = = = G ± A A A A e. Find B ˆ when α = 2.0. ( ) ( 1.0, 2.0,3.0) 0.27, 0.53,0.80 14 = = = − G ± B B B

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(Worksheet B) f. Find ( A + B ) ( ) 2 ( ) 30 5.0 5.0 25 5.0 α α + = + = + − + = + G G G G G A A B A A B g. Find α so that | A × B | = 30 and the x -component of A × B is negative. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 ˆ ˆ ˆ 2.0 5.0 1.0 1.0 3.0 ˆ ˆ ˆ 15 1.0 6.0 2.0 5.0 ˆ ˆ ˆ 15 5.0 2.0 5.0 We want 15 5.0 2.0 5.0 30 5 50 625 0 10 125 0 Solutions: 5 150 But we also want 15 0, so the answer is α α α α α α α α α α α
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Recitation Worksheet B Solutions - Worksheet B Vectors 1...

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