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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 2 · Q23
Find the co-ordinates of foot of perpendicular drawn from (0,0,0) to line x/1=(y +1)/-1=(z -3)/-2.
Find the co-ordinates of foot of perpendicular drawn from $\displaystyle (0,0,0)$ to line $\displaystyle \frac{x}{1}=\frac{\mathrm{y}+1}{-1}=\frac{\mathrm{z}-3}{-2}$.
Marking-scheme solution
DRs of $\displaystyle PQ$ are $\displaystyle \langle\lambda,-\lambda-1,3-2 \lambda\rangle$
DRs of line $\displaystyle l$ are $\displaystyle \langle 1,-1,-2\rangle$
$\displaystyle PQ \perp l$
$\displaystyle \Rightarrow 1 \cdot \lambda-1(-\lambda-1)-2(3-2 \lambda)=0 \Rightarrow \lambda=\dfrac{5}{6}$
Coordinates of $\displaystyle Q\left(\dfrac{5}{6},-\dfrac{11}{6}, \dfrac{4}{3}\right)$
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