The angle between the lines (3-x)/(-7) = (y+5)/(-5) = z/1 and x/1 = y/2 = z/3 is: Option 1: /4 Option 2: /3 Option 3: /2 Option 4: /6

Answer: /2. Solution: Rewrite (3-x)/(-7)=(x-3)/7, so direction ratios are 7,-5,1. Dot with 1,2,3: 7-10+3=0. Since the dot product is zero, the angle is ()/2.

Geometry

3D Geometry

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The angle between the lines $\dfrac{3-x}{-7} = \dfrac{y+5}{-5} = \dfrac{z}{1}$ and $\dfrac{x}{1} = \dfrac{y}{2} = \dfrac{z}{3}$ is:

$\pi/4$

$\pi/3$

$\pi/2$

$\pi/6$

✅ Correct Option: 3

Rewrite $\dfrac{3-x}{-7}=\dfrac{x-3}{7}$ , so direction ratios are $\langle 7,-5,1\rangle$ .

Dot with $\langle 1,2,3\rangle$ : $7-10+3=0$ .

Since the dot product is zero, the angle is $\dfrac{\pi}{2}$ .

2026: 29 May Shift 2

P is a point on the line segment joining the points (3, 2, -1) and (6, 2, -2) internally. If x coordinate of P is 5, then its z-coordinate is

2022: 16 July Shift 2

The two lines given by $\vec{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \mu(\hat{i} - \hat{j} + \hat{k})$ and $\vec{r} = (2\hat{i} - \hat{j} - \hat{k}) + \mu(-\hat{i} + \hat{j} - \hat{k})$

A. are perpendicular

B. are parallel.

C. have shortest distance 0.

D. have shortest distance $\sqrt{26}$ .

E. have shortest distance $\sqrt{78}$ .

Which of the above statements are true?

Choose the correct answer from the options given below:

2025: 26 May Shift 2

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

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

Choose the correct answer from the options given below:

2022: 10 Aug Shift 1

The distance of the plane $\vec{r} \cdot \left(\frac{2}{7}\hat{i} + \frac{3}{7}\hat{j} - \frac{6}{7}\hat{k}\right) = 2$ from the origin is

2022: 17 Aug Shift 2

The direction ratio's of line of intersection of two planes :

$2x + y + z + 47 = 0$ and $3x - 2y - z + 41 = 0$ are :

The angle between the lines 3−x−7=y+5−5=z1\dfrac{3-x}{-7} = \dfrac{y+5}{-5} = \dfrac{z}{1}−73−x​=−5y+5​=1z​ and x1=y2=z3\dfrac{x}{1} = \dfrac{y}{2} = \dfrac{z}{3}1x​=2y​=3z​ is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The angle between the lines $\dfrac{3-x}{-7} = \dfrac{y+5}{-5} = \dfrac{z}{1}$ and $\dfrac{x}{1} = \dfrac{y}{2} = \dfrac{z}{3}$ is: