Question

At what angle the two vectors of magnitude p + q and p - q should act so the resultant is

Answer 1

Use formula in link with F1 = P+Q and F2 = P-Q.

R = √[F1² + F2² + 2F1.F2.cos(α)] 

. . = √[(P+Q)² + (P-Q)² + 2(P+Q)(P-Q)cosα] 

. . = √[P²+2PQ+Q² + P²-2PQ+Q² + 2(P²-Q²)cosα] 

. . = √[2P² + 2Q² + 2(P²-Q²)cosα] 

We want R = √[P² + Q²] 

√[P² + Q²] = √[2P² + 2Q² + 2(P²-Q²)cosα] 

P² + Q² = 2P² + 2Q² + 2(P²-Q²)cosα 

2(P²-Q²)cosα = -P² – Q² 

cosα = (-P² – Q²)/(2(P²-Q²)) 

. . . . .= (P² + Q²)/(2(Q² – P²)) 

Answer 2

Explanation:

hope you have understood