Question

The resultant of $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${\overrightarrow{R}}_1$ . On reversing the vector $\overrightarrow{B}$ , the resultant becomes ${\overrightarrow{R}}_2$ . The value of $R_1^2+R_2^2$ is :

• A. $A^2+B^2$
• B. $A^2-B^2$
• C. $2(A^2+B^2)$
• D. $2(A^2-B^2)$

Answer 1

Answer: (C)

$2(A^2+B^2)$

$\overrightarrow{A}+\overrightarrow{B}={\overrightarrow{R}}_1$ and $\overrightarrow{A}-\overrightarrow{B}={\overrightarrow{R}}_2$

$\Rightarrow R_1^2+R_2^2=(A^2+B^2+2ABcos\theta )+(A^2+B^2-2ABcos\theta )$
$=2(A^2+B^2)$