Calculate the dot product of $\mathbf{a}=2\mathbf{i}+3\mathbf{j}+4\mathbf{k}$ and $\mathbf{b}=-\mathbf{i}+5\mathbf{j}$.

Step-by-step solution

1. Write the components of $\mathbf{a}$ as $(2,3,4)$ and of $\mathbf{b}$ as $(-1,5,0)$ (missing component is 0).
2. Multiply corresponding components: $2\times (-1)=-2$, $3\times 5=15$, $4\times 0=0$.
3. Add the products: $-2+15+0=13$.
4. Therefore, $\mathbf{a}\cdot \mathbf{b}=13$.

Concept tested: Dot product of vectors

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