CUET Mathematics 2025 - If the direction ratios of two lines are a, b, c and (b-c), (c-a), (a-b) respectively, then the angle between these lines is: | PYQs + Solutions

2025: 26 May Shift 2

If the points (-1, -1, 2), (2, m, 5) and (3, 11, 6) are collinear, then m equals

2022: 30 Aug Shift 1

The shortest distances of the point $(1, 2, 3)$ from $x$ , $y$ , $z$ axes respectively are

2026: 29 May Shift 1

A line in space is uniquely determined if

(A) It passes through a given point and has a given direction.

(B) It passes through two given points.

(C) It passes through a given point.

(D) It has a given direction.

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2026: 30 May Shift 1

Given a line $L:\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ , then

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. The foot of perpendicular from point (1, 6, 3) on line L	I. $2\sqrt{13}$
B. Perpendicular distance from point (1, 6, 3) to line L	II. (1, 0, 7)
C. Image of point (1, 6, 3) with respect to line L	III. (1, 3, 5)
D. Distance between points (1, 6, 3) and (1, 0, 7)	IV. $\sqrt{13}$

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2025: 22 May Shift 2

Match List-I with List-II

List-I	List-II
Equation of line	Information
(A) $\vec{r} = (3\hat{i} - 2\hat{j} + \hat{k}) + \lambda(\hat{j} - 2\hat{k})$	(I) Direction ratios are 2, 4, -1
(B) $\frac{2-x}{1} = \frac{2y+1}{4}$ , $z = 2$	(II) Perpendicular to $2\hat{i} - \hat{j} + \hat{k}$
(C) $\frac{x}{1} = \frac{y-3}{2} = \frac{3-4z}{2}$	(III) Passing through the point $(3, -2, 1)$
(D) $\vec{r} = (3\hat{i} + 2\hat{j} + \hat{k}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$	(IV) Direction ratios are -1, 2, 0

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2026: 22 May Shift 1

Direction cosines of 2 lines are given by the equations $3l+m+5n=0, 6mn-2nl+5lm=0$ then which of the following statements are correct ?

(A) Direction ratios of two lines are (1, 2, -1) and (-2, 1, 1).

(B) Angle between lines is $\frac{\pi}{3}$ .

(C) The angle between the lines is $\cos^{-1}\left(-\frac{1}{6}\right)$ .

(D) Vectors parallel to these lines are $\hat i+2\hat j-\hat k$ and $-2\hat i+\hat j+\hat k$ .

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If the direction ratios of two lines are $a, b, c$ and $(b-c), (c-a), (a-b)$ respectively, then the angle between these lines is: