Find the scalar (dot) product of vectors $\mathbf{a}=2\mathbf{i}-\mathbf{j}+4\mathbf{k}$ and $\mathbf{b}=-3\mathbf{i}+5\mathbf{j}+\mathbf{k}$.

Step-by-step solution

1. Write the components: $\mathbf{a}=(2,-1,4)$ and $\mathbf{b}=(-3,5,1)$.
2. Multiply corresponding components: $2(-3)=-6$, $(-1)(5)=-5$, $4(1)=4$.
3. Add the three products: $-6+(-5)+4=-7$.
4. Thus the dot product $\mathbf{a}\cdot \mathbf{b}=-7$.

Concept tested: Scalar (dot) product

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