Question

Let $\overline{a},\overline{b},\overline{c}$ be vectors of length $3,4$ and $5$ respectively. Find the length of the vector $|\overline{a}+\overline{b}+\overline{c}|$. if they are mutually perpendicular.

Answer 1

$|\overline{a}|=3|\overline{b}|=4|\overline{c}|=5$

Since they are perendicular

$|\overline{a}+\overline{b}+\overline{c}|\sqrt{(a^2+b^2+c^2)}\sqrt{9+16+25}\sqrt{50}=5\sqrt{2}$