Question

If $|\overrightarrow{a}|=6,|\overrightarrow{b}|=8,|\overrightarrow{a}-\overrightarrow{b}|=10,$ then $|a+b|$ is equal to:

• A. 10
• B. 24
• C. 40
• D. 36
• E. 20

Answer 1

Answer: (A)

$\because$ $|\overrightarrow{a}-\overrightarrow{b}{|}^2={\overrightarrow{a}}^2+{\overrightarrow{b}}^2-2\overrightarrow{a}.\overrightarrow{b}$ $\Rightarrow$ $100=36+64-2\overrightarrow{a}.\overrightarrow{b}$ $\Rightarrow$ $\overrightarrow{a}.\overrightarrow{b}=0$ $\therefore$ $|\overrightarrow{a}+\overrightarrow{b}{|}^2={\overrightarrow{a}}^2+{\overrightarrow{b}}^2+2\overrightarrow{a}.\overrightarrow{b}$ $=36+64+0=100$ $\Rightarrow$ $|\overrightarrow{a}+\overrightarrow{b}|=10$