Question

A vector has 3 unit length and equal components. The vector is

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

Answer 1

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

Let the vector be $a\hat{i}+a\hat{j}+a\hat{k}$

Since the length of vector is 3,

So, $\sqrt{a^2+a^2+a^2}=3$

$\to \sqrt{3}a=3$

$\to a=\sqrt{3}$

Thus, the vector is $\sqrt{3}(\hat{i}+\hat{j}+\hat{k}).$

The correct answer is C.