What is the magnitude of the vector $\mathbf{v}=7\mathbf{i}-24\mathbf{j}$?

Step-by-step solution

1. Write the components of $\mathbf{v}$ as $(7,-24)$.
2. Square each component: $7^2=49$ and $(-24{)}^2=576$.
3. Add the squared values: $49+576=625$.
4. Take the square root of the sum: $\sqrt{625}=25$.
5. Thus, the magnitude of $\mathbf{v}$ is $25$.

Concept tested: Magnitude of a vector

Published 12 September 2026 · How this solution was prepared and checked