Question

The number of vectors of unit length perpendicular to vectors $\overrightarrow{a}=\hat{i}+\hat{j}$ and $\overrightarrow{b}=\hat{j}+\hat{k}$ is

• A. 1
• B. 2
• C. 3
• D. none

Answer 1

Answer: (B)

2

let the vector be

$\overrightarrow{C}=C_1\hat{i}+C_2\hat{j}+C_3\hat{k}$

$\overrightarrow{a}.\overrightarrow{b}=0\Rightarrow C_1+C_2=0$

$\overrightarrow{b}.\overrightarrow{c}=0\Rightarrow C_2+C_3=0$

$\overrightarrow{C}=-C_2\hat{i}+C_2\hat{j}-C_2\hat{k}$

$\left|\overrightarrow{C}\right|=1$

$\therefore \sqrt{3C_2^2}=1\Rightarrow C_2=\pm \frac{1}{\sqrt{3}}$