CUET Mathematics - The direction cosines of a line equally inclined with the co-ordinate axes are | PYQs + Solutions

CUET Mathematics 2025 13 May Shift 2

Geometry

Medium

core

$(1,1,1)$

$\left(\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\right)$

$\left(\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}\right)$

$\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

✅ Correct Option: 3

Related questions:

15 May Shift 1

Consider the lines $l_1: \frac{x-1}{0} = \frac{y-1}{1} = \frac{2-z}{1}$ and $l_2: \frac{x}{2} = \frac{y}{0} = \frac{2z-1}{4}$ , then which of the following are correct?

(A) Direction Ratio's of $l_1 = <0, 1, 1>$

(B) Direction Ratio's of $l_2 = <2, 0, 2>$

(D) Angle between $l_1$ and $l_2 =$ $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

26 May Shift 2

A line passes through the point with position vector $2\hat{i} - \hat{j} + 4\hat{k}$ and is in the direction of the vector $\hat{i} + \hat{j} - 2\hat{k}$ . The equation of the line in Cartesian form is:

3 June Shift 2

The angle at which the line, $\frac{x-1}{0} = \frac{2-y}{-1} = \frac{2z-3}{-2}$ is inclined with the positive direction of z-axis is

CUET Mathematics 2025 13 May Shift 2 PYQs

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