Question

The resultant of two vectors p and q is r. If q is doubl3d

Answer 1

Let the angle between two vectors P and Q be α and their resultant is R

So we can write

R2 = P 2 + Q2 + 2PQ cos α......[1]

When Q is doubled then let the resultant vector be R1 , So we can write

R2

1 = P 2 + 4Q 2 + 4PQ cos α......[2]

Again by the given condition R1 is perpendicular to P

So 4Q 2 = P 2 + R2

1 ......[3]

Combining [2] and [3] we get

R2

1 = P 2 + P 2 + R2

1 + 4PQ cos α

⇒ 2PQ cos α = − P 2 ......[4]

combining [1] and [4] we get

R2 = P 2 + Q2 − P 2

⇒ R = Q