A vector $\vec{r}=a \hat{i}+b \hat{j}$ is equally inclined to both $x$ and $y$ axes. If the magnitude of the vector is 2 units, then what are the values of $a$ and $b$ respectively?

• A

  $\frac{1}{2}, \frac{1}{2}$
• B

  $\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$
• Correct answer
  C

  $\sqrt{2}, \sqrt{2}$
• D

  $2$, $2$

Solution

$|\vec{r}|=\sqrt{a^2+b^2}=2$ $\Rightarrow a^2+b^2=4\ldots$ (i) As $\vec{r}$ is equally inclined to both axis, $\therefore a=b \text {. }$ Again from equation (i), $a^2+a^2=4 \Rightarrow a=\sqrt{2}=b$

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