First slide

Vectors

Question

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

Moderate

A

90°
B

45°
C

180°
D

0°

Solution

Suppose two vectors are P and Q.
It is given that
$|P + Q| = |P - Q|$
Let angle between P and Q is $ϕ$ .
$∴ P^{2} + Q^{2} + 2 P Q \cos ϕ = P^{2} + Q^{2} - 2 P Q \cos ϕ$
$\Rightarrow 4 P Q \cos ϕ = 0$
$\Rightarrow \cos ϕ = 0 (∵ P, Q \neq 0)$
$\Rightarrow ϕ = \frac{π}{2} = 90 °$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App