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Vector A has a magnitude of 4.00m and a direction of 15.0degrees. Vector B has a...

Vector A has a magnitude of 4.00m and a direction of 15.0degrees. Vector B has a magnitude of 6.00m and a direction of 147.0degrees. Vector C=B-A. What are the magnitude and direction of vector C?
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Answer #1

A = 4 cos 15 i + 4sin 15 j

= 3.863i + 1.035j

B = -6cos (180-147)i + 6 sin (180-147)j

= -5.032i + 3.267j

C = B - A

= (-5.032i+3.267j) + (3.863i + 1.035j)

= -1.17i + 4.3j

magnitude = sqrt(1.17^2 +4.3^2) = 4.46 m

angle = 180 - tan^-1(1.17 / 4.3)=164.77o

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