Scalar projection of the line segment joining the points $\mathrm{A}(-2,0,3), \mathrm{B}(1,4,2)$ on the line whose direction ratios are $6,-2,3$ is

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Aicharya · Accepted Answer

Let $\bar{a}$ be the vector joining $\mathrm{A}(-2,0,3)$ and $\mathrm{B}(1,4,2)$. $\begin{aligned} & 	herefore \quad \overline{\mathrm{a}}=(1-(-2)) \hat{\mathrm{i}}+(4-0) \hat{\mathrm{j}}+(2-3) \hat{\mathrm{k}} \ & =3 \hat{i}+4 \hat{j}-\hat{k} \ & 	ext { and } \bar{b}=6 \hat{i}-2 \hat{j}+3 \hat{k} \ & 	herefore \quad 	ext { Projection }=\frac{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}{|\overline{\mathrm{b}}|}=\frac{3 	imes 6+4 	imes(-2)-1 	imes 3}{\sqrt{6^2+(-2)^2+3^2}} \ & =\frac{18-8-3}{\sqrt{49}} \ & =\frac{7}{7} \ & =1 \ & \end{aligned}$

Scalar projection of the line segment joining the points $\mathrm{A}(-2,0,3), \mathrm{B}(1,4,2)$ on the line…

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