Three Dimensional Geometry PYQs - Last 10 Years
VITEEE / Mathematics / Algebra / 15 recent questions
MathematicsAlgebra2016-2025
Practice 15 VITEEE 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.
15
PYQs on Page
Mathematics / Algebra
2021-2025
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Based on indexed question metadata
15
Last 5 Years
2021-2025
15
Last 10 Years
2016-2025
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15PYQs
MCQ100%
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#1 Unknown15
15 in last 5 years15 in last 10 years
Last 10 Years Three Dimensional Geometry Questions
Showing 15 of 15 filtered questions.
1Three Dimensional Geometry
The equation of the straight line through the origin and parallel to the line
$$ \begin{aligned} & (b+c) x+(c+a) y+(a+b) z=k= \\ & (b-c) x+(c-a) y+(a-b) z \text { is } \end{aligned} $$
$$ \begin{aligned} & (b+c) x+(c+a) y+(a+b) z=k= \\ & (b-c) x+(c-a) y+(a-b) z \text { is } \end{aligned} $$
MCQ+4 / -12025
2Three Dimensional Geometry
The distance between the point with position vector $-\hat{i}-5 \hat{j}-10 \hat{k}$ and the point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ with the plane $x-y+z=5$, is $\_\_\_\_$ (units)
MCQ+4 / -12025
3Three Dimensional Geometry
The value of ' $a$ ' for which the lines $\frac{x-2}{1}=\frac{y-9}{2}=\frac{z-13}{3}$ and $\frac{x-a}{-1}=\frac{y-7}{2}$ $=\frac{z+2}{-3}$ intersect, is
MCQ+4 / -12024
4Three Dimensional Geometry
If the distance between the planes $8 x+12 y-14 z=2$ and $4 x+6 y-7 z=2$ can be expressed as $\frac{1}{\sqrt{N}}$, then the value of $\frac{N(N+1)}{2}$ is
MCQ+4 / -12024
5Three Dimensional Geometry
If \(\theta_1, \theta_2\) and \(\theta_3\) are the angles made by a line with the positive direction of \(X, Y\) and \(Z\)-axes, then \(\cos 2 \theta_1+\cos 2 \theta_2+\cos 2 \theta_3\) is equal to
MCQ+4 / -12023
6Three Dimensional Geometry
The plane is perpendicular to the planes \(x-y+2 z-4=0\) and \(2 x-2 y+z=0\) and passes through \((1,-2,1)\) is
MCQ+4 / -12023
7Three Dimensional Geometry
The distance between the point \((7,2,4)\) and the plane determined by the points \((2,5,-3),(-2,-3,5)\) and \((5,3,-3)\) is
MCQ+4 / -12023
8Three Dimensional Geometry
The image of the point \((2,3,7)\) in the plane \(2 x+5 y-3 z-19=0\), is
MCQ+4 / -12023
9Three Dimensional Geometry
The image of the point \((2,-3,4)\) with respect to the plane \(4 x+2 y-4 z+3=0\), is
MCQ+4 / -12022
10Three Dimensional Geometry
If a variable plane cuts the coordinate axes in \(A, B, C\) and is at constant distance $p$ from the origin, then the locus of the centroid of the tetrahedron \(A B C\) is equal to
MCQ+4 / -12022
11Three Dimensional Geometry
A force of magnitude \(\sqrt{6}\) acting along, the line joining points \(A(2,-1,1)\) and \(B(3,1,2)\) displaces a particle from \(A\) to \(B\). The work done by the force is
MCQ+4 / -12022
12Three Dimensional Geometry
The position vector of a point \(R\) which divides the line joining \(P(6,3,-2)\) and \(Q(3,1,-4)\) in the ratio \(2 : 1\) externally is
MCQ+4 / -12021
13Three Dimensional Geometry
The angle between the lines \(\frac{x-5}{-3}=\frac{y+3}{-4}=\frac{z-7}{0}, \frac{x}{1}=\frac{y-1}{-2}=\frac{z-6}{2}\) is
MCQ+4 / -12021
14Three Dimensional Geometry
The following lines are
$$\begin{aligned}
\mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda^{\prime}(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}), \\
\text { and } \quad \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu...
$$\begin{aligned}
\mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda^{\prime}(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}), \\
\text { and } \quad \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu...
MCQ+4 / -12021
15Three Dimensional Geometry
If \((3,4,-1)\) and \((-1,2,3)\) be end points of the diameter of a sphere, then the radius of the sphere is
MCQ+4 / -12021