## Problem on finding the length of vectors

Find the length of the 2d vector $2 \ \bfi + 3 \ \bfj$ and the 3d vector $\langle2, 3, 4 \rangle$.
• ## Solution

Recall that
For the vector $2 \ \bfi + 3 \ \bfj$, we identify that $x_1 = 2$ and $x_2 = 3$.
The length of $2 \ \bfi + 3 \ \bfj$ is $$\left | 2 \ \bfi + 3 \ \bfj \right | = \sqrt{2^2 + 3^2} = \sqrt{13}.$$
Recall that
We get $$\left | \langle 2, 3, 4 \rangle \right | = \sqrt{2^2 + 3^2 + 4^2} = \sqrt{29}.$$