Question

A vector has $3$ units of length and equal components on co-ordinate axes. The vector is

• A. $(\hat{i}+\hat{j}+\hat{k})$
• B. $\sqrt{2}(\hat{i}+\hat{j}+\hat{k})$
• C. $\sqrt{3}(\hat{i}+\hat{j}+\hat{k})$
• D. $\sqrt{5}(\hat{i}+\hat{j}+\hat{k})$

Answer 1

The correct option is C $\sqrt{3}(\hat{i}+\hat{j}+\hat{k})$

Let the vector be $a\hat{i}+a\hat{j}+a\hat{k}$
Since the length of vector is $3$
So, $\sqrt{a^2+a^2+a^2}=3$
Squaring both sides,
$a^2+a^2+a^2=9$
$3a^2=9$
$a=\pm \sqrt{3}$
Required vector $=\pm (\sqrt{3}\hat{i}+\sqrt{3}\hat{j}+\sqrt{3}\hat{k})$