Question

If $\vec{a}, \vec{b}, \vec{c}$ are any three mutually perpendicular vectors of equal magnitude a, then $|\vec{a} + \vec{b} + \vec{c}|$

• A. $a$
• B. $2a$
• C. $3a$
• D. $\sqrt{2}a$

Hint:

For perpendicular vectors, $|\vec{a}+\vec{b}+\vec{c}|^2 = |\vec{a}|^2+|\vec{b}|^2+|\vec{c}|^2$.

Answer 1

The Correct Option is C

Step 1: $|\vec{a} + \vec{b} + \vec{c}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2 = a^2 + a^2 + a^2 = 3a^2$.}
Step 2: So $|\vec{a} + \vec{b} + \vec{c}| = \sqrt{3}a$. Option (C) is $3a$, which is incorrect. Correct is $\sqrt{3}a$ not in options.}