The co-ordinates of the foot of the perpendicular from the point $(0,2,3)$ on the line $\frac{x+3}{5}=\frac{y+1}{2}=\frac{z+4}{3}$ is

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Aicharya · Accepted Answer

Let $\frac{x+3}{5}=\frac{y+1}{2}=\frac{z+4}{3}=\lambda$ Any point on the line is $P \equiv(5 \lambda-3,2 \lambda-1,3 \lambda-4)$
Given point is $\mathrm{A}(0,2,3)$ $\therefore \quad$ The d.r.s. of AP are $5 \lambda-3,2 \lambda-3,3 \lambda-7$ Since the line $A P$ is perpendicular to the given line. $\begin{array}{ll} \therefore \quad & 5(5 \lambda-3)+2(2 \lambda-3)+3(3 \lambda-7)=0 \\ & \Rightarrow 38 \lambda-42=0 \\ & \Rightarrow \lambda=\frac{21}{19} \\ \therefore \quad & P \equiv\left(\frac{48}{19}, \frac{23}{19}, \frac{-13}{19}\right) \end{array}$

The co-ordinates of the foot of the perpendicular from the point $(0,2,3)$ on the line…

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