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Question

a vector a which has magnitude 8 is added to a vector B which lies on x-axis. The sum of these two vectors, lies on y-axis and has a magnitude twice of the magnitude of B. The magnitude of vector B is

Joshi sir comment

let a = 8cosAi+8sinAj and B = bi

sum of the two = 8cosAi+8sinAj+bi

it is given as 2bj

so 8cosAi+8sinAj+bi = 2bj

so (8cosA+b)i+8sinAj = 2bj

now on comparing coefficient of i and j we get

cosA = -b/8 and sinA = 2b/8

now use sin²A +cos²A = 1

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