If vectors a, b and c are mutually perpendicular vectors such that |a|=|b|=10,|c|=1, then the length of vector 2a + 2b + 40c is

Question

If vectors $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are mutually perpendicular vectors such that $|\mathbf{a}|=|\mathbf{b}|=10,|\mathbf{c}|=1$, then the length of vector $2 a+2 b+40 c$ is

(a) 20

(b) $20 \sqrt{6}$

(c) $40 \sqrt{6}$

(d) None of these

Answer 1

Since, $\mathbf{a}, \mathbf{b}$ and c are mutually perpendicular vectors.

Let, $\mathbf{a}=10 \mathbf{i}, \quad \mathbf{b}  =10 \mathbf{j}, \quad \mathbf{c}=\mathbf{k}$

$\therefore  |2 \mathbf{a}+2 \mathbf{b}+40 \mathrm{c}|  =|20 \mathbf{i}+20 \mathbf{j}+40 \mathbf{k}|$

$ =|20(i+j+2 \mathbf{k})|=20 \sqrt{6}$

So, The correct option of this question will be (B).