Question

Find the magnitude of the projection of〈-4,-4⟩ onto the vector ⟨−1,−6⟩

Answer 1

`(28√(37))/(37) \approx 4.6\; \sf (nearest\;tenth)`

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 = 〈-1, -6⟩
• v = 〈-4, -4⟩

Calculate the magnitude of vector u:

`\implies |u|=√((-1)^2+(-6)^2)=√(37)`

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|)=(\langle -1, -6\rangle \cdot \langle-4, -4\rangle)/(√(37))=(4 +24)/(√(37))=(28)/(√(37))=(28√(37))/(37)`