The diagram below shows two vectors, A and B, and their angles relative to the c

Question

The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as Indicated. DAT A: o= 45.1degree Beta = 54.6 degree (A) = 2.1 cm. The vector A - B Is parallel to the -x axis (points due West). Calculate the v-component or vector B. Since the sum vector (A-B) has no y-component, vector A must have the same y-component as vector B. As shown, ' east' Is for +x, and north for +y, thus the answer can be negative. Calculate the x component of the vector A - B Calculate the magnitude of the vector A + B.

Explanation / Answer

A = 2.1 cos 45.1 i + 2.1 sin45.1 j

B = C cos 144.6 i + C sin 144.6 j ( where C is the magnitude of B)

A-B =  (2.1 cos 45.1- C cos 144.6 )i + (2.1 sin45.1- C sin 144.6)j

(2.1 sin45.1- C sin 144.6) j = 0

1.487 - C 0.579 = 0

C = 1.487/ 0.579 = 2.568

Y component of B = 2.568 sin 144.6 = 1.487 cm apprx

b) y component of A = 1.487 cm

c) x component of A-B = (2.1 cos 45.1- C cos 144.6 )i= (2.1 cos 45.1- 2.568 cos 144.6 )i = 3.5753 i

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