Three Dimensional Geometry PYQs - Last 5 Years
VITEEE / Mathematics / Algebra / 15 recent questions
MathematicsAlgebra2021-2025
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
Year Range
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 5 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