Question

Find the magnitude of the projection:

Answer 1

3

Explanation:

`\boxed{\begin{minipage}{7 cm}\underline{Scalar projection}\\\\Scalar projection $=(u \cdot v)/(|u|)$\\\\where:\\ \phantom{ww}$\bullet$ $u$ is the vector being projected onto.\\\end{minipage}}`

Given:

• u = 〈0, -1⟩
• v = 〈-5, -3⟩

Calculate the magnitude of vector u:

`\implies |u|=√((0)^2+(-1)^2)=1`

The scalar projection is the magnitude of the vector projection.

Therefore, the magnitude of the projection of vector v onto vector u is:

`\implies (u \cdot v)/(|u|)=(\langle0, -1\rangle \cdot \langle-5, -3\rangle)/(1)=(0 +3)/(1)=(3)/(1)=3`