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