please help In the vector diagram below, the magnitudes and directions of two of

Question

please help

In the vector diagram below, the magnitudes and directions of two of the vectors are given. The magnitude and direction of the third vector (dashed arrow) is unknown, but it is to be in a direction and of a magnitude to give zero resultant -- in other words, to completely cancel out the effects of the other two vectors. Calculate the magnitude and direction of this third vector, expressing your answer both in Cartesian and Polar forms. (You may find using some "non-calculator" trig function values very useful for common angles like 30 degree, 60 degree etc.)

Explanation / Answer

let the vector be V and the angle it makes with x-axis is theta .

V cos theta = - 3 cos 30 + 2sqrt 3 cos 60

and V sin theta= - 3 sin30+2sqrt3 sin60

solving this ,

theta = 120 ,

V = sqrt 3

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