Three Dimensional Geometry PYQs - Last 5 Years

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Practice 88 TS EAMCET 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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Last 5 Years Three Dimensional Geometry Questions

Showing 38 of 88 filtered questions.

1Three Dimensional Geometry

A plane $\pi$ passing through the point $(1,1,1)$ is perpendicular to the line joining the points $(6,3,2)$ and $(1,-4,-9)$. If $a x+b y+c z-23=0$ is the equation of the plane $\pi$, then $a+b-c=$

2Three Dimensional Geometry

Equation of the plane through the mid-point of the line segment joining the points $A(4,5,-10)$ and $B(-1,2,1)$ and perpendicular to $A B$ is

3Three Dimensional Geometry

If the direction cosines $(l, m, n)$ of two lines are connected by the relations $l+m+n=0$ and $l m=0$, then the angle between those lines is

4Three Dimensional Geometry

The sum of the squares of the perpendicular distances of a point $(x, y, z)$ from the coordinate axes is $k$ times the square of the distance of the point from the origin Then, $k=$

5Three Dimensional Geometry

If $M$ is the foot of the perpendicular drawn from $P($ -1,2,-1 ) to the plane passing through the point $A(3,-2,1)$ and perpendicular to the vector $4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$, then the length of $P M$ is

6Three Dimensional Geometry

A line $L$ is parallel to both the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If line $L$ makes an angle $\alpha$ with the positive direction of $X$-axis, then $\cos \alpha=$

7Three Dimensional Geometry

If $A=(1,-1,2), B=(3,4,-2), C=(0,3,2)$ and $D=(3$, $5,6)$, then the angle between the lines $\mathbf{A B}$ and $\mathbf{C D}$ is

8Three Dimensional Geometry

Consider the following statements:
Assertion (A) : The direction ratios of a line $L_1$ are 2,5, 7 and the direction ratios of another line $L_2$ are $\frac{4}{\sqrt{19}}$, $\frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. Then, the lines $L_1,...

9Three Dimensional Geometry

Let $L$ be a line passing through the points $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+6 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$. Let $P$ be a plane passing through $-5 \hat{\mathbf{i}}+19 \hat{\mathbf{j}...

10Three Dimensional Geometry

Let $A(2,3,-1), B(4,1,0), C(-1,-1,1)$ be the vertices of a $\triangle A B C$. Let $D$ be the point where the bisector of $B A C$ meet the side $B C$. Then, the direction ratios of $A D$ are

11Three Dimensional Geometry

If $\mathbf{r} \cdot(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=5, \mathbf{r} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})=7$ are two planes and $(16,-9,0)$ is a point common to both the planes, then the vector e...

12Three Dimensional Geometry

If a plane passing through the points $(2,3,0),(0,-5,2)$ and ( $-2,0,3$ ) meets the $X, Y$ and $Z$-axes in $A, B$ and $C$ respectively, then $A=$

13Three Dimensional Geometry

$A(1,1,1), B(1,-4,3), C(2,-2,0)$ and $D(8,1,4)$ are the vertices of a tetrahedron. $G_1, G_2, G_3$ and $G_4$ are the centroids of the faces $A B C, B C D, C D A$ and $D A B$. Then, the centroid of the tetrahedron having $G_1, G_2, G_3$ and ...

14Three Dimensional Geometry

Let $A=(1,2,0), B=(2,0,-1), C=(0,-2,3)$ and $D=(-1,2,-3)$ be four points in the space. Let $G_1$ be the centroid of $\triangle A B C$ and $G_2$ be the centroid of tetrahedron $A B C D$. If $P$ divides, $G_1 G_2$ in the ratio $4: 3$ internal...

15Three Dimensional Geometry

If $l, m$ and $n$ are the d.c.'s of a normal to the plane passing through the points $(0,1,2)$, $(3,0,2)$ and $(4,5,0)$, then $|I|+|m|+|n|=$

16Three Dimensional Geometry

If $\mathbf{r}=(2-\lambda+\mu) \hat{\mathbf{i}}+(1-\mu) \hat{\mathbf{j}}+(2-3 \lambda+2 \mu) \hat{\mathbf{k}}$ is the vector equation of a plane, then the equivalent cartesian equation of the plane is

17Three Dimensional Geometry

If the d.r.'s of two lines are connected by the relations $a-b+c=0, a^2-b^2+2 c^2=0$ and $\theta$ is the angle between these lines, then $\cos \theta=$

18Three Dimensional Geometry

Let $\pi_1$ be a plane passing through the point $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and perpendicular to the vector $-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$. Let the line $L$ passing through the points $3 \hat{\mathbf{i}}-2 ...

19Three Dimensional Geometry

Let $D$ be the foot of the perpendicular drawn from the point $A(2,0,3)$ to the line joining the points $B(0,4,1)$ and $C(-2,0,4)$. Then, the ratio in which $D$ divides $B C$ is

20Three Dimensional Geometry

Let $6 x-3 y+2 z-6=0$ be the given plane. If $a, b$ and $c$ are the intercepts made by the plane on $X, Y$ and $Z$-axes, respectively; $l, m$ and $n$ are the direction cosines of a normal drawn to the plane and $p$ is the perpendicular dist...

21Three Dimensional Geometry

If $A(1,2,3), B(2,-3,1), C(3,2,-1)$ are three vertices of a tetrahedron $A B C D$ and $G\left(\frac{5}{2}, \frac{3}{2}, \frac{9}{4}\right)$ is its centroid, then the point which divides $G D$ in the ratio $1: 2$ is

22Three Dimensional Geometry

A bisector of the angle between the normals of the planes $4 x+3 y=5$ and $x+2 y+2 z=4$ is along the vector

23Three Dimensional Geometry

Let $L$ be a line passing through a point $A$ and parallel to the vector $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. Let $-7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}$ be the position vector of a point $P$ on $L$...

24Three Dimensional Geometry

If a plane $x+y+z-5=0$ intersects the line joining $A(1,1,1)$ and $B(2,2,2)$ at $P$, then $A P: P B=$

25Three Dimensional Geometry

If the angle between the planes $\mathbf{r} \cdot(11 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\alpha \hat{\mathbf{k}})=7$ and $\mathbf{r} \cdot(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})=5$ is $\frac{\pi}{2}$, then $\alpha=$

26Three Dimensional Geometry

Let $A(2,5,7)$ be the image of the point $B(1,-2,3)$ with respect to a plane $\pi$. Let $C$ be the point where $A B$ meets the plane $\pi$. Let $D=(2,1,6)$. Then, the direction cosines of $C D$ are

27Three Dimensional Geometry

The point which lies on the plane passing through the point $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}},-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$ is

28Three Dimensional Geometry

$A(27,-243,81)$ is a point in space, $B, C$ and $D$ are images of $A$ with respect to $X Y, Y Z$ and $Z X$ planes respectively. If the centroid of the $\triangle B C D$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma=$

29Three Dimensional Geometry

Let the foot of the perpendicular drawn from the point $(1,2,3)$ to a plane be $(-1,3,-2)$. Then, the perpendicular distance from the origin to the plane is

30Three Dimensional Geometry

Let $A(1,2,3), B(-1,4,6), C(0,-6,4)$ and $D(1,1,1)$ be the vertices of a tetrahedron, $G$ be its centroid and $G_1$ be the centroid of its face $B C D$. Then, $\frac{A G_1}{A G}=$

31Three Dimensional Geometry

The cartesian equation of the plane passing through the point $(1,-2,3)$ and perpendicular to the vector $-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$, is

32Three Dimensional Geometry

If a line $L$ is common to the planes $x-y+z+2=0$ and $2 x+y-2 z+5=0$ then the direction cosines of the line $L$ are

33Three Dimensional Geometry

If $P$ is a point on the line parallel to the vector $2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ and passing through the point $A$ whose position vector is $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $A P=21$...

34Three Dimensional Geometry

Let $\pi_1^{\prime}$ be the plane passing through the point $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and perpendicular to the vector $a \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\pi_2$ be the plane passing t...

35Three Dimensional Geometry

Let a plane $P$ has the points $\hat{\mathbf{i}}, \hat{\mathbf{j}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$. Let $L$ be the line through the point $A$ and parallel to the vector $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\math...

36Three Dimensional Geometry

If the points $A(1,3,5), B(2,4,6), C(4,5, k)$ form a right angled triangle then the number of possible values of $k$ is

37Three Dimensional Geometry

A plane containing two lines whose direction ratios are $(-1,2,1)$ and $(1,3,2)$ passes through the point $(2,1, k)$. If this plane also passes through the point $(3,-1,4)$, then $k=$

38Three Dimensional Geometry

Let $A=(3,4,0), B=(4,4,4), C=(-6,2,3)$ and $D=(1,1,2)$. If $\theta$ is the acute angle between the lines $A B$ and $C D$, then $\cos \theta=$