Question

If $\overrightarrow{a}\mathrm{and}\overrightarrow{b}$are two unit vectors such that
$\overrightarrow{a}=\hat{i}$ and $\overrightarrow{b}=\hat{j}$
then the angle between

$\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$ is

• A.
  $0^o$
• B.
  ${90}^o$
• C.
  ${180}^o$
• D.
  ${45}^o$

Answer 1

The correct option is B

${90}^o$
We need to find angle between $\overrightarrow{a}+\overrightarrow{b}and\overrightarrow{a}-\overrightarrow{b}$
Using dot product of vectors,
$\left(\hat{i}+\hat{j}\right).\left(\hat{i}-\hat{j}\right)=\left(|\hat{i}+\hat{j}|\right)\left(|\hat{i}-\hat{j}|\right)\cos \theta$

$\Rightarrow \cos \theta =\frac{\left(\hat{i}+\hat{j}\right).\left(\hat{i}-\hat{j}\right)}{\left(|\hat{i}+\hat{j}|\right)\left(|\hat{i}-\hat{j}|\right)}=0$​​​​
By doing the calculations we get the value of $\cos \theta$ as 0, so the angle will be 90°.