Geometry

3D Geometry

Medium

core

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

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{2\pi}{3}$

$\frac{3\pi}{4}$

✅ Correct Option: 1,4

Solution Coming Soon

2022: 23 Aug Shift 1

The angle between the pairs of lines

$\vec{r} = (3\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(\hat{i} + 2\hat{j} + 2\hat{k})$

$\vec{r} = (5\hat{i} - 2\hat{j}) + \mu(3\hat{i} + 2\hat{j} + 6\hat{k})$ is :

2026: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) The distance of a point $P(a,b,c)$ from x-axis	(I) $\sqrt{a^2+b^2+c^2}$
(B) The distance of a point $P(a,b,c)$ from y-axis	(II) $\sqrt{b^2+c^2}$
(C) The distance of a point $P(a,b,c)$ from Z-axis	(III) $\sqrt{a^2+c^2}$
(D) The distance of a point $P(a,b,c)$ from origin	(IV) $\sqrt{a^2+b^2}$

Choose the correct answer from the options given below:

2025: 29 May Shift 2

The vector equation of line passing through (2, -1, 3) and perpendicular to the lines

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

(Here $\lambda$ is a parameter)

2023: 15 June Shift 2

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

2022: 25 May Shift 1

The angle between the line $\frac{x+2}{3} = \frac{y-3}{2} = \frac{z+5}{6}$ and the plane $2x + 10y - 11z = 5$ is:

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

The angle at which the line, x−10=2−y−1=2z−3−2\frac{x-1}{0} = \frac{2-y}{-1} = \frac{2z-3}{-2}0x−1​=−12−y​=−22z−3​ is inclined with the positive direction of z-axis is