Question

At what angle two forces (P+Q) and (P-Q) act so that resultant is root 2(P square +Q square)

Answer 1

Answer:

The angle between the two vectors will be  cos^(-1)(2(P^2+Q^2))^2-  ((P+Q)^2 + (P-Q)^2 ] / 2(P+Q)(P-Q)

Explanation:

we know that

R^2 = P^2 + Q^2 + 2PQcosθ

Therefore

cosθ = [R^2 - (P^2 + Q^2 ] / 2PQ

here

P = (P+Q)  

Q = (P-Q)

R = 2(P^2+Q^2)

so, we have

cosθ = (2(P^2+Q^2))^2-  ((P+Q)^2 + (P-Q)^2 ] / 2(P+Q)(P-Q)

so, the angle between the two vectors will be

θ= cos^(-1)(2(P^2+Q^2))^2-  ((P+Q)^2 + (P-Q)^2 ] / 2(P+Q)(P-Q)