Geometry

3D Geometry

Easy

core

Equation of a line passing through (1, 2, -3) which is parallel to the line $\frac{x+2}{3} = \frac{y-3}{-4} = \frac{z+5}{5}$ is

$\frac{x+1}{3} = \frac{y+2}{-4} = \frac{z-3}{5}$

$\frac{x-1}{3} = \frac{y-2}{-4} = \frac{z+3}{5}$

$\frac{x-3}{1} = \frac{y+4}{2} = \frac{z-5}{-3}$

$\frac{x+3}{1} = \frac{y-4}{2} = \frac{z+5}{-3}$

✅ Correct Option: 2

A parallel line has the same direction ratios $3, -4, 5$ .

Through $(1,2,-3)$ the equation is $\frac{x-1}{3} = \frac{y-2}{-4} = \frac{z+3}{5}$ .

2025: 26 May Shift 2

The value of p so that the lines $\frac{x-1}{-3} = \frac{2y-2}{2p} = \frac{z-3}{2}$ and $\frac{x-1}{-3p} = \frac{y-1}{4} = \frac{6-z}{5}$ are at right angles is

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Line : $x = 2y + 1 = z - 1$	(I) Crosses $xz$ plane at (1, 0, 1)
(B) Line : $x + 1 = 2y + 1 = z$	(II) Crosses $xz$ plane at (0, 0, 1)
(C) Line : $x - 1 = 2y = z + 1$	(III) Crosses $xz$ plane at (1, 0, -1)
(D) Line : $x - 1 = 2y = z - 1$	(IV) Crosses $xz$ plane at (1, 0, 2)

Choose the correct answer from the options given below:

2025: 14 May Shift 2

The angle between the lines

$l_1: \frac{x + 1}{1} = \frac{2 - y}{2} = \frac{z - 1}{1}$ and $l_2: \frac{x - 1}{4} = \frac{2y - 4}{6} = \frac{z - 1}{2}$ is

2026: 19 May Shift 1

If $\theta$ is the angle between the lines $L_1$ and $L_2$ , whose direction cosines are $l_1, m_1, n_1$ and $l_2, m_2, n_2$ respectively, then

Match List-I with List-II

List-I	List-II
(A) $\cos\theta$	(I) $l_1l_2+m_1m_2+n_1n_2$
(B) $\sin\theta$	(II) $l_1l_2+m_1m_2+n_1n_2=0$
(C) $L_1$ and $L_2$ are perpendicular	(III) $\frac{l_1}{l_2}=\frac{m_1}{m_2}=\frac{n_1}{n_2}$
(D) $L_1$ and $L_2$ are parallel	(IV) $\sqrt{\sum(m_1n_2-m_2n_1)^2}$

Choose the correct answer from the options given below:

2026: 26 May Shift 2

The value of $\lambda$ so that the lines $\dfrac{1-x}{3} = \dfrac{7y-14}{2\lambda} = \dfrac{z-3}{2}$ and $\dfrac{7-7x}{3\lambda} = \dfrac{y-5}{1} = \dfrac{6-z}{5}$

are at right angles is:

2025: 19 May Shift 1

Distance of the point $(2, 4, -1)$ from the line $\frac{10+2x}{2} = \frac{y+3}{4} = \frac{6-z}{9}$ is

Equation of a line passing through (1, 2, -3) which is parallel to the line x+23=y−3−4=z+55\frac{x+2}{3} = \frac{y-3}{-4} = \frac{z+5}{5}3x+2​=−4y−3​=5z+5​ is

Solution

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Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Equation of a line passing through (1, 2, -3) which is parallel to the line $\frac{x+2}{3} = \frac{y-3}{-4} = \frac{z+5}{5}$ is