The resultant of two vectors `vec(P)` and `vec(Q)` is `vec(R)`. If `vec(Q)` is doubled then the new resultant vector is perpendicular to `vec(P)`. Then magnitude of `vec(R)` is :-

Options

A. `((P^(2)-Q^(2))/(2PQ))`
B. Q
C. `P/Q`
D. `(P+Q)/(P-Q)`

Answer

B

Explanation

When Q is doubled then `vecQ ` becomes `2vecQ` . Suppose that the new resultant becomes `vecR`.
From , `tan alpha = (Bsin theta)/(A+B cos theta ) implies tan 90^(@) = (2Q sin theta ) / (P + 2Q cos theta) `
`implies 1/0 = (2Q sin theta) / (P + 2Q cos theta)`
`implies 2Q cos theta = - P :. cos theta = - P / (2Q) " "....(i) `
Now according to question ,
`R = sqrt(P^(2)+Q^(2) +2PQ(-(P)/(2Q)))`
`implies R = sqrt(P^2+Q^2-P^2)`
`implies R = sqrt(Q^2) :. R = Q`