Question

If $\left(\overrightarrow{A}\&\overrightarrow{B}\right)$ are two vectors then find $(\overrightarrow{A}+2\overrightarrow{B}).(2\overrightarrow{A}-3\overrightarrow{B})$.If $\theta$ is the angle between them.

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

$(\overrightarrow{A}+2\overrightarrow{B}).(2\overrightarrow{A}-3\overrightarrow{B})=2\overrightarrow{A}.\overrightarrow{A}-3\overrightarrow{A}.\overrightarrow{B}+4\overrightarrow{B}.\overrightarrow{A}-6(\overrightarrow{B}.\overrightarrow{B})$

= $2(\overrightarrow{A}.\overrightarrow{A})-3ABcos\theta +4ABcos\theta -6(\overrightarrow{B}.\overrightarrow{B})=2A^2+ABcos\theta -6B^2$