Question

If ${\overrightarrow{a}}_{1}$ and ${\overrightarrow{a}}_{2}$are two non collinear unit vectors and if $|{\overset{\rightarrow}{a}}_{1} + {\overset{\rightarrow}{a}}_{2}|$= $\sqrt{3}$, then the value of $({\overset{\rightarrow}{a}}_{1} - {\overset{\rightarrow}{a}}_{2})$. $(2{\overset{\rightarrow}{a}}_{1} + {\overset{\rightarrow}{a}}_{2})$ is –

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

Answer 1

Answer: (C)

$\frac{1}{2}$

Answer 2

a₁ = a₂ = 1 and

$a_{1}^{2}$+ $a_{2}^{2}$+ 2a₁a₂ cosq = $(\sqrt{3})^{2}$= 3

Or 1+ 1+ 2cosq = 3 or cosq = $\frac{1}{2}$

Now $({\overrightarrow{a}}_{1} - {\overrightarrow{a}}_{2})$ $(2{\overrightarrow{a}}_{1} + {\overrightarrow{a}}_{2})$ = $2a_{1}^{2}$ –$a_{2}^{2}$– a₁a₂ cosq

= 2 – 1 – $\frac{1}{2}$= $\frac{1}{2}$