Question

When two vectors of magnitudes P and Q are inclined at an angle ∅ the magnitude of their resultant 2P. When the inclination is
changed to 180 – ∅ the magnitude of the resultant is halved. Find the ratio of P to Q.

Answer 1

In case 1

Resultant R = (P²+ Q²+ 2PQcosΦ)^(1/2)

4P²= P² + Q² +2PQcosΦ

3P² - Q² = 2PQcosΦ

2nd case

P² = P² + Q² +2PQcos(180-Φ)

-Q² = -2PQcosΦ

Q/P= cosΦ

substituting in 1st case

3P² -Q² = 2Q²

3P² = 3Q²

P/Q = 1