First slide

Vectors

Question

The resultant of $\vec{A} + \vec{B}$ is ${\vec{R}}_{1}$ . On reversing the vector $\vec{B}$ , the resultant becomes ${\vec{R}}_{2}$ . What is the value of ${\vec{R}}_{1}^{2} + {\vec{R}}_{2}^{2}$ ?

Moderate

A

$A^{2} + B^{2}$
B

$A^{2} - B^{2}$
C

$2 (A^{2} + B^{2})$
D

$2 (A^{2} - B^{2})$

Solution

${\vec{R}}_{1} = \vec{A} + \vec{B}$ , ${\vec{R}}_{2} = \vec{A} - \vec{B}$
$R_{1}^{2} + R_{2}^{2} = (A^{2} + B^{2} {+2ABcosθ)}^{} +(A^{2} + B^{2} {-2ABcosθ)}^{}$
= $2 (A^{2} + B^{2})$

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