Question

The resultant of two vectors → and → is → . If Q is doubled, the new resultant is perpendicular to P. Then R equals (a) P (b) (P+Q) (c) Q (d) (P–Q)

Answer 1

Answer:

Q

Explanation:

From, parallelogram law of vector addition,

$tan\beta = \frac{Qsin\theta}{P + Qcos\theta}$

Where, β is angle between R and P

θ = angle between P and Q

When Q is doubled,

tan90 = 0

P + 2Qcosθ = 0

cosθ = -P/2Q

according to cosine law,

R² = P² + Q² + 2PQcosθ

$R^2 = P^2 + Q^2 + 2PQ(\frac{-P}{2Q})\\R^2 = P^2 + Q^2 - P^2\\R^2 = Q^2$

R = Q