Find the magnitude of the vector $\mathbf{v}=5\mathbf{i}+12\mathbf{j}-9\mathbf{k}$.

Step-by-step solution

1. Take the components of $\mathbf{v}$: $(5,12,-9)$.
2. Square each component: $5^2=25$, $12^2=144$, $(-9{)}^2=81$.
3. Add the squares: $25+144+81=250$.
4. Take the square root of the sum: $\sqrt{250}=5\sqrt{10}$.
5. Thus the magnitude of $\mathbf{v}$ is $5\sqrt{10}$.

Concept tested: Magnitude of a 3‑D vector

Published 15 September 2026 · How this solution was prepared and checked