Question

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two non collinear unit vectors and $|\overrightarrow{a}+\overrightarrow{b}|=\sqrt{3}$, then $(2\overrightarrow{a}-5\overrightarrow{b}).(3\overrightarrow{a}+\overrightarrow{b})=$

• A. $\frac{13}{2}$
• B. $\frac{11}{2}$
• C. $0$
• D. $-\frac{11}{2}$

Answer 1

The correct option is D $-\frac{11}{2}$

$|\overrightarrow{a}+\overrightarrow{b}{|}^2$

$=(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{a}+\overrightarrow{b})=|\overrightarrow{a}{|}^2+2\overrightarrow{a}.\overrightarrow{b}+|\overrightarrow{b}{|}^2$

$=3$

Since, $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors

$\therefore ,$ $\overrightarrow{a}.\overrightarrow{b}=1/2$

$(2\overrightarrow{a}-5\overrightarrow{b}).(3\overrightarrow{a}+\overrightarrow{b})$

$=6|\overrightarrow{a}{|}^2-5|\overrightarrow{b}{|}^2-13\overrightarrow{a}.\overrightarrow{b}$

$=1-\frac{13}{2}$

$=\frac{-11}{2}$