The direction ratios of the line (1-x)/3 = (7y - 14)/2 = (z-3)/2 are Option 1: -3, 1/7, 2 Option 2: -3, 2, 2 Option 3: -3, 2/7, 1 Option 4: -21, 2, 14

Answer: -21, 2, 14. Solution: Rewrite in standard symmetric form (x-x_0)/a = (y-y_0)/b = (z-z_0)/c: (x-1)/(-3) = (y-2)/(2/7) = (z-3)/2. Direction ratios are (-3, 2/7, 2). Multiplying by 7 gives the proportional set (-21, 2, 14).

Geometry

3D Geometry

Medium

The direction ratios of the line $\frac{1-x}{3} = \frac{7y - 14}{2} = \frac{z-3}{2}$ are

$-3, \frac{1}{7}, 2$

$-3, 2, 2$

$-3, \frac{2}{7}, 1$

$-21, 2, 14$

✅ Correct Option: 4

Rewrite in standard symmetric form $\frac{x-x_0}{a} = \frac{y-y_0}{b} = \frac{z-z_0}{c}$ : $\frac{x-1}{-3} = \frac{y-2}{2/7} = \frac{z-3}{2}$ . Direction ratios are $(-3, 2/7, 2)$ . Multiplying by 7 gives the proportional set $(-21, 2, 14)$ .

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. $\sqrt{13}$

Choose the correct answer from the options given below:

2026: 31 May Shift 2

If the lines $x = ay+b$ , $z = cy+d$ and $x = py+q$ , $z = ry+s$ are perpendicular, then $ap + cr$ is equal to

2022: 25 May Shift 1

If a line makes angles 90 degree, 60 degree and $\theta$ with $x, y$ and $z$ axis respectively, where $\theta$ is acute, then value of $\theta$ is:

2026: 18 May Shift 2

The angle between the two lines whose direction cosines are given by the equations $4l+m+n=0$ and $2mn+24nl+4lm=0$ , is

2023: 15 June Shift 2

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is :

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

The direction ratios of the line 1−x3=7y−142=z−32\frac{1-x}{3} = \frac{7y - 14}{2} = \frac{z-3}{2}31−x​=27y−14​=2z−3​ are

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CUET Mathematics Past Year Questions (Topic-Wise)

The direction ratios of the line $\frac{1-x}{3} = \frac{7y - 14}{2} = \frac{z-3}{2}$ are