Parametrize: (t−5,4t−3,−9t+6). Vector from this to (2,4,−1): (7−t,7−4t,−7+9t). Perpendicular to (1,4,−9): (7−t)+4(7−4t)−9(−7+9t)=0⇒7−t+28−16t+63−81t=0⇒98−98t=0, t=1. Foot: (−4,1,−3).
CUET UG 2022 — Mathematics Geometry
The foot of perpendicular from point (2,4,−1) on the line 1x+5=4y+3=−9z−6 is :
Held on 17 Aug 2022 · Verified 13 Jul 2026.
(−4,1,−3)
(4,1,−3)
(4,1,3)
(4,−1,3)
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Consider the line $\vec{r} = -2\hat{i} + 3\hat{j} + \hat{k} + \lambda(5\hat{i} - 3\hat{j} - \hat{k})$. Match List-I with List-II | List-I | List-II | |---|---| | (A) A point on the given line | (I) $\left(\frac{5}{\sqrt{35}}, \frac{-3}{\sqrt{35}}, \frac{-1}{\sqrt{35}}\right)$ | | (B) Direction ratios of the given line | (II) (2, 3, 1) | | (C) Direction cosines of the given line | (III) (5, -3, -1) | | (D) Direction ratios of a line perpendicular to given line | (IV) (-2, 3, 1) | Choose the correct answer from the options given below:
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