Question

If $e_1$ and $e_2$ are non-collinear unit vectors,compute $(2e_1-5e_2).(3e_1+e_2)$ if $|e_1+e_2|=\sqrt{3}.$

• A. $\frac{11}{2}$
• B. $\frac{-11}{2}$
• C. $\frac{-9}{2}$
• D. $\frac{9}{2}$

Answer 1

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

Given, $|e_1+e_2|=\sqrt{3}$
Squaring both side, we get
${(e_1+e_2)}^2=3\Rightarrow 1+1+2e_1.e_2=3$ $\therefore e_1.e_2=1/2$
$\therefore (2e_1-5e_2).(3e_1+e_2)=6e_1^2-5e_2^2-13e_1.e_2=6-5-\frac{13}{2}=-\frac{11}{2}$