Question

The resultant of two vectors P and Q given by R²=P²+Q².what is the angle between them

Answer 1

$\mathbb{\bold {ANSWER}}$

Angle between the vectors P and Q is 90°

$\mathbb{\bold {EXPLANATION}}$

Given that,

P and Q are two vectors

Let, Ф be the angle between P and Q

       R be the resultant of P and Q

We know that, the resultant of P and Q is given by

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

Squaring both sides we get,

$R^2 = P^2 + Q^2+2PQcos\phi$

Given that,

R² = P² + Q²

Substituting this value in we get,

P² + Q² = P² + Q² + 2PQcosФ

P² + Q² - P² - Q² = 2PQcosФ

2PQcosФ = 0

cosФ = 0

Ф = 90°