Question

If $\overrightarrow{a_1}$ and $\overrightarrow{a_2}$ are two two non-collinear unit vectors , then the value of $(\overrightarrow{a_1}-\overrightarrow{a_2}).(\overrightarrow{2a_1}+\overrightarrow{a_2})$ which is not possible is

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

Answer 1

The correct option is D $1$

Given ${\overrightarrow{a}}_1$ and ${\overrightarrow{a}}_2$ are non collinear

Now $({\overrightarrow{a}}_1-{\overrightarrow{a}}_2).(2{\overrightarrow{a}}_1+{\overrightarrow{a}}_2)$

$2{|{\overrightarrow{a}}_1|}^2+{\overrightarrow{a}}_1{\overrightarrow{a}}_2-2{\overrightarrow{a}}_1{\overrightarrow{a}}_2-{|{\overrightarrow{a}}_2|}^2$

$2-{\overrightarrow{a}}_1{\overrightarrow{a}}_2-1$

$1-{\overrightarrow{a}}_1{\overrightarrow{a}}_2$

Now to check for collinear

$1-{\overrightarrow{a}}_1{\overrightarrow{a}}_2=0$

${\overrightarrow{a}}_1{\overrightarrow{a}}_2=1$

Thus the value of $({\overrightarrow{a}}_1-{\overrightarrow{a}}_2).(2{\overrightarrow{a}}_1+{\overrightarrow{a}}_2)$

can never be 1