Let $\overrightarrow{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}, a_i>0, i=1,2,3$ be a vector which makes equal angles with the coordinate axes $OX,OY$ and $OZ$. Also, let the projection of $\overrightarrow{a}$ on the vector $3\hat{i}+4\hat{j}$ be $7$ . Let $\overrightarrow{b}$ be a vector obtained by rotating $\overrightarrow{a}$ with $90°$. If $\overrightarrow{a},\overrightarrow{b}$ and $x$-axis are coplanar, then projection of a vector $\overrightarrow{b}$ on $3\hat{i}+4\hat{j}$ is equal to

• A

  $\sqrt{7}$
• Correct answer
  B

  $\sqrt{2}$
• C

  $2$
• D

  $7$

Hence, the correct answer is option: 'B'.