Question

If $a_1$ and $a_2$ are two non-collinear unit vectors and if $|a_1+a_2|=\sqrt{3}$ ,then the value of $(a_1-a).(2a_1+a_2)$ is

• A. 2
• B. $\frac{3}{2}$
• C. $\frac{1}{2}$
• D. 1

Answer 1

Answer: (C)

Since, $a_1$ and $a_2$ are non-collinear
$\therefore a_1=a_2=1$
and $|a_1+a_2|=\sqrt{3}$
$\Rightarrow a_1^2+a_2^2+2a_1{a}_2\cos \theta =(\sqrt{3}{)}^2$
$\Rightarrow 1+1+2\cos \theta =3\Rightarrow \cos \theta =\frac{1}{2}$
Now $(a_1+a_2).(2a_1+a_2)$
$20mm=2a_1^2-a_2^2-a_1{a}_2\cos \theta =2-1-\frac{1}{2}=\frac{1}{2}$