Find the magnitude of the vector $\mathbf{u}=5\mathbf{i}-12\mathbf{j}+0\mathbf{k}$.

Step-by-step solution

1. Write the components of $\mathbf{u}$ as $(5,-12,0)$.
2. Square each component: $5^2=25$, $(-12{)}^2=144$, $0^2=0$.
3. Add the squares: $25+144+0=169$.
4. Take the square root of the sum: $\sqrt{169}=13$.
5. Hence the magnitude is $13$.

Concept tested: Magnitude of a vector

Published 8 September 2026 · How this solution was prepared and checked