## Problem on vector length

Find the length of the vector from $(2,4,5)$ to $(3, -1, -2)$.
• ## Solution

First we find the vector from $(2,4,5)$ to $(3,-1,-2)$. Then, we compute it's length.
Recall that
The vector from $(2,4,5)$ to $(3, -1, -2)$ is thus $$(3,-1,-2) -(2,4,5) = (1, -5, -7).$$
Recall that
The length of the vector from $(2,4,5)$ to $(3, -1, -2)$ is thus $$\sqrt{1^2 + (-5)^2 + (-7)^2} = \sqrt{75}.$$