Question

if R=P+Q and R^2 = P^2 + Q^2 , find the angle between P and Q



Right answer will be marked as brillianist and wrong or inappropriat answer will be reported​

Answer 1

Answer:

Angle between P and Q = 90° or π/2 rad

Explanation:

Given that,

$\vec{R}=\vec{P}+\vec{Q}$

$R^{2} =P^{2} +Q^{2}$   --------(1)

Hence, we find out that

R is the resultant of P and Q

Let, angle between P and Q be α

To find the resultant of {tex} \vec{P} {\tex} and {tex} \vec{Q} {\tex} , we know

$\boxed{R = \sqrt{P^{2} + Q^{2}+2PQcos\alpha } }$

Squaring both sides we get,

R² = P² + Q² + 2PQcosα --------(2)

Substituting (1) in (2)

P² + Q² = P² + Q² + 2PQcosα

2PQcosα = 0

cosα = 0

α = 90° or π/2 rad