Question

If a, b, c are mutually perpendicular unit vectors, then $|\mathbf{a} + \mathbf{b} + \mathbf{c}| =$

• A. $\sqrt{3}$
• B. 3
• C. 1
• D. 0

Answer 1

Answer: (A)

$\sqrt{3}$

Answer 2

Three mutually perpendicular unit vectors $= \mathbf{a}$, $\mathbf{b}$and $\mathbf{c}$.

Therefore $|\mathbf{a}| = |\mathbf{b}| = |\mathbf{c}| = 1$ and $\mathbf{a}.\mathbf{b} = \mathbf{b}.\mathbf{c} = \mathbf{c}.\mathbf{a} = 0$.

We know that

$|\mathbf{a} + \mathbf{b} + \mathbf{c}|^{2} = (\mathbf{a} + \mathbf{b} + \mathbf{c}).(\mathbf{a} + \mathbf{b} + \mathbf{c}) = |\mathbf{a}|^{2} + |\mathbf{b}|^{2}$

$+ |\mathbf{c}|^{2} + 2(\mathbf{a}.\mathbf{b} + \mathbf{b}.\mathbf{c} + \mathbf{c}.\mathbf{a}) = 1 + 1 + 1 + 0 = 3$

or $|\mathbf{a} + \mathbf{b} + \mathbf{c}| = \sqrt{3}.$