Three Dimensional Geometry PYQs - Last 5 Years

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MathematicsAlgebra2022-2026

All Three Dimensional Geometry PYQs Last 10 Years Create chapter test

Practice 20 KCET Mathematics questions from Three Dimensional Geometry. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Mathematics / Algebra

2022-2026

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Last 5 Years Three Dimensional Geometry Questions

Showing 20 of 20 filtered questions.

1Three Dimensional Geometry

The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is

2Three Dimensional Geometry

The measure of the angle between the lines $x = k + 1, y = 2k - 1, z = 2k + 3, k \in \mathbb{R}$ and $\dfrac{x - 1}{2} = \dfrac{y - 2}{1} = \dfrac{z - 3}{1}$ is

3Three Dimensional Geometry

The three points $A(2, 4, 3), B(4, a, 9)$ and $C(10, -1, 7)$ form a right-angled triangle with $\angle B = 90^\circ$, then the value of "a" is

4Three Dimensional Geometry

The distance of the point $\mathrm{P}(-3,4,5)$ from yz plane is

5Three Dimensional Geometry

The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{-2}$ is

6Three Dimensional Geometry

If a line makes angles $90^{\circ}, 60^{\circ}$ and $\theta$ with $\mathrm{x}, \mathrm{y}$ and z axes respectively, where $\theta$ is acute, then the value of $\theta$ is

7Three Dimensional Geometry

The plane containing the point $(3,2,0)$ and the line $\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$ is

8Three Dimensional Geometry

The equation $x y=0$ in three-dimensional space represents

9Three Dimensional Geometry

If lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\frac{x-1}{3 k}=\frac{y-5}{1}=\frac{z-6}{-5}$ are mutually perpendicular, then $k$ is equal to

10Three Dimensional Geometry

The distance between the two planes $2 x+3 y+4 z=4$ and $4 x+6 y+8 z=12$ is

11Three Dimensional Geometry

The sine of the angle between the straight line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{4-z}{-5}$ are the plane $2 x-2 y+z=5$ is

12Three Dimensional Geometry

If \((2,3,-1)\) is the foot of the perpendicular from \((4,2,1)\) to a plane, then the equation of the plane is

13Three Dimensional Geometry

The point of intersection of the line \(x+1=\frac{y+3}{3}=\frac{-z+2}{2}\) with the plane \(3 x+4 y+5 z=10\) is

14Three Dimensional Geometry

The equation of the plane through the points \((2,1,0),(3,2,-2)\) and \((3,1,7)\) is

15Three Dimensional Geometry

The length of perpendicular drawn from the point \((3,-1,11)\) to the line \(\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) is

16Three Dimensional Geometry

If a line makes an angle of \(\frac{\pi}{3}\) with each \(X\) and \(Y\) axis, then the acute angle made by \(\mathrm{Z}\)-axis is

17Three Dimensional Geometry

The distance of the point whose position vector is \((2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})\) from the plane \(\mathbf{r} \cdot(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=4\) is

18Three Dimensional Geometry

The angle between the pair of lines \(\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}\) and \(\frac{x+1}{1}=\frac{y-4}{4}=\frac{z-5}{2}\) is

19Three Dimensional Geometry

The coordinates of foot of the perpendicular drawn from the origin to the plane \(2 x-3 y+4 z=29\) are

20Three Dimensional Geometry

The octant in which the point (2, \(-\)4, \(-7\)) lies is