General point on line: Q=(2t−1,−2t+3,−t).
PQ=(2t−2,−2t+1,−t+3).
PQ perpendicular to direction (2,−2,−1):
2(2t−2)−2(−2t+1)−1(−t+3)=9t−9=0, so t=1.
Q=(1,1,−1).
The foot of perpendicular from the point P (1, 2, -3) to the line x+1 2 = y-3 -2 = z -1 is
CUET UG 2022 — Mathematics Geometry
2022mcqmedium
The foot of perpendicular from the point P (1, 2, -3) to the line 2x+1=−2y−3=−1z is
Official previous-year question
Held on 6 Aug 2022 · Verified 13 Jul 2026.
Options
- A
(1,1,1)
- B
(1,−1,1)
- C
(1,1,−1)
- D
(−1,1,1)
Did you get this right?
Sign in to track your attempts and accuracy.
Your note
Sign in to keep a private note on this question. Nothing you write is ever public.
CUET UG Geometry in other years
More CUET UG Geometry questions
Consider $f(x) = \sin(3x) + 4, \forall x \in \mathbb{R}$. Then (A) Maximum value of $f(x)$ is 5 (B) Minimum value of $f(x)$ is 3 (C) Maximum value of $f(x)$ is attained at $x = \frac{\pi}{6}$ (D) Minimum value of $f(x)$ is attained at $x = 0$ Choose the correct answer from the options given below:
2025medium
The maximum value of $\sin x \cdot \cos x$ is:
2025easy
The angle between the pair of lines given by $\vec{r} = \hat{i} + 2\hat{j} - 3\hat{k} + \lambda (\hat{i} - 2\hat{j} + 2\hat{k})$ and $\vec{r} = 5\hat{i} + \hat{j} + \hat{k} + \mu (3\hat{i} - 2\hat{j} + 6\hat{k})$ is
2025medium
The minimum value of the function $f(x) = 3\sin x - 4\cos x, x \in [-4\pi, 4\pi]$ is equal to
2025medium
Acute angle between the lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{5}$ and $\frac{x-1}{4} = \frac{y+1}{-3} = \frac{z+10}{5}$ is:
2025medium
Other Mathematics topics for CUET UG
Keep practicing Geometry
Work through every CUET UG Geometry PYQ, year by year.