Vector Algebra PYQs - Last 5 Years

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All Vector Algebra PYQs Last 10 Years Create chapter test

Practice 99 TS EAMCET Mathematics questions from Vector Algebra. 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 Vector Algebra Questions

Showing 50 of 99 filtered questions.

1Vector Algebra

If the volume of a tetrahedron having $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+p \hat{\mathbf{k}}$ as its coterminous edges is ...

2Vector Algebra

$A B C D$ is a tetrahedron, $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}},-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$, $3 \bar{i}+2 \bar{j}-\bar{k}$ are the the position vectors of the points $A, B$ and $C$ respective...

3Vector Algebra

Let $\mathbf{a}$ and $\mathbf{b}$ be two vectors such that $|\mathbf{a}|=|\mathbf{b}|$ and $|\mathbf{a}+2 \mathbf{b}|=|2 \mathbf{a}-\mathbf{b}|$. If $\mathbf{c}$ is a vector parallel to $\mathbf{a}$, then the angle between $\mathbf{b}$ and ...

4Vector Algebra

If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $|\mathbf{a}|=|\mathbf{b}|=\sqrt{6}$ and $\mathbf{a} \cdot \mathbf{b}=-1$, then $|\mathbf{a} \times \mathbf{b}| \sin (\mathbf{a}, \mathbf{b})=$

5Vector Algebra

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \mathbf{b}=6 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{c}=-4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$ are three vectors, then $\sqr...

6Vector Algebra

Two adjacent sides of a triangle are represented by the vectors $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $2 \sqrt{3} \hat{\mathbf{i}}-2 \sqrt{3} \hat{\mathbf{j}}+\sqrt{3} \hat{\mathbf{k}}$. Then, the least angle of the t...

7Vector Algebra

In a quadrilateral $A B C D, \mathbf{A}=\frac{2 \pi}{3}$ and $A C$ is the bisector of angle $\mathbf{A}$. If $15|\mathbf{A C}|=5|\mathbf{A D}|=3|\mathbf{A B}|$, then angle between $\mathbf{A B}$ and $\mathbf{B C}$ is

8Vector Algebra

Consider the following
Assertion (A) The two lines $\mathbf{r}=\mathbf{a}+t(\mathbf{b})$ and $\mathbf{r}=\mathbf{b}+s(\mathbf{a})$ intersect each other.
Reason (R) The shortest distance between the lines $\mathbf{r}=\mathbf{p}+t(\mathbf{q})...

9Vector Algebra

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three non- coplanar and mutually perpendicular vectors of same magnitude $K . r$ is any vectors satisfying $\mathbf{a} \times((\mathbf{r}-\mathbf{b}) \times \mathbf{a})+\mathbf{b} \times((\mathbf{r}-...

10Vector Algebra

A plane $\pi_1$ contains the vectors $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$. Another plane $\pi_2$ contains the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$ and $3 \hat{\mathbf{i}}+2 \hat{\mathbf{k}}$...

11Vector Algebra

$7 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}, \hat{\mathbf{i}}-6 \hat{\mathbf{j}}+10 \hat{\mathbf{k}},-\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are the positi...

12Vector Algebra

Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+p \hat{\mathbf{k}}$ be two vectors.
If $(\mathbf{a}, \mathbf{b})=60^{\circ}$, then $p=$

13Vector Algebra

If $\mathbf{a}=\hat{\mathbf{i}}+\sqrt{11} \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+\sqrt{11} \hat{\mathbf{j}}-10 \hat{\mathbf{k}}$ are two vectors, then the component of $\mathbf{b}$ perpendicular to $\mathbf{a}...

14Vector Algebra

If $\mathbf{a}=(x+2 y-3) \hat{\mathbf{i}}+(2 x-y+3) \hat{\mathbf{j}}$ and $\mathbf{b}=(3 x-2 y) \hat{\mathbf{i}} +(x-y+1) \hat{\mathbf{j}}$ are two vectors such that $\mathbf{a}=2 \mathbf{b}$, then $y-5 x=$

15Vector Algebra

In a $\triangle A B C$, if $\mathbf{B C}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{C A}=6 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$, then the perimeter of the triangle is

16Vector Algebra

$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, a_1 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}+c_1 \hat{\mathbf{k}}, a_2 \hat{\mathbf{i}}+b_2 \hat{\mathbf{j}}+c_2 \hat{\mathbf{k}}, a_3 \hat{\mathbf{i}}+b_3 \hat{\mathbf{j}}+c_3 \hat{\mathbf{...

17Vector Algebra

Let $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{c}=6 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ be three vectors. If $\mathbf{d}$ is...

18Vector Algebra

Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ be three vectors. If $\mathbf...

19Vector Algebra

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{b}=9 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}-18 \hat{\mathbf{k}}$ are two vectors, then $\frac{\text { Projection of } \mathbf{b} \text { on } \mathbf{a}}{\text...

20Vector Algebra

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are two vectors, then $(\mathbf{a}+2 \mathbf{b}) \times(3 \mathbf{a}-\mathbf{b})$

21Vector Algebra

If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=12$ and $|\mathbf{a}-\mathbf{b}|=13$, then $|2 \mathbf{a}+\mathbf{b}|=$

22Vector Algebra

The point of intersection of the line joining the points $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and the plane passing through the points $\hat{\mathbf{i}}, 2 \hat{\mathbf...

23Vector Algebra

The position vectors of two points $A$ and $B$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $7 \hat{\mathbf{i}}-\hat{\mathbf{k}}$ respectively. The point $P$ with position vector $-2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5...

24Vector Algebra

$A, B, C$ and $D$, are any four points. If $E$ and $F$ are mid-points of $A C$ and $B D$ respectively, then $\mathbf{A B}+\mathbf{C B}+\mathbf{C D}+\mathbf{A D}=$

25Vector Algebra

$O(0,0,0), A(3,1,4), B(1,3,2)$ and $C(0,4,-2)$ are the vertices of a tetrahedron. If $G$ is the centroid of the tetrahedron and $G_1$ is the centroid of its face $A B C$, then the point which divides $G G_1$ in the ratio $1: 2$ is

26Vector Algebra

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three unit vectors such that $x \mathbf{a}+y \mathbf{b}+z \mathbf{c}= p(\mathbf{b} \times \mathbf{c})+q(\mathbf{c} \times \mathbf{a})+r(\mathbf{a} \times \mathbf{b})$. If $(\mathbf{a}, \mathbf{b})=(\...

27Vector Algebra

If $a=|\mathbf{a}| ; b=|\mathbf{b}|$, then $\left(\frac{\mathbf{a}}{a^2}-\frac{\mathbf{b}}{b^2}\right)^2$

28Vector Algebra

The four points whose position vectors are given by $2 a+3 b-c, a-2 b+3 c, 3 a+4 b-2 c$ and $a-6 b+6 c$ are

29Vector Algebra

$\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are the position vectors of the vertices $A, B$ and $C$ of a $\triangle ...

30Vector Algebra

If $\theta$ is the angle between the vectors $4 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$, then $\sin 2 \theta=$

31Vector Algebra

$\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three vectors such that $|a|=3,|b|=2 \sqrt{2},|c|=5$ and $\mathbf{c}$ is perpendicular to the plane of $\mathbf{a}$ and $\mathbf{b}$. If the angle between the vectors a and $\mathbf{b}$ is $\fra...

32Vector Algebra

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are non-coplanar vectors and the points $\lambda \mathbf{a}+3 \mathbf{b}-\mathbf{c}, \mathbf{a}-\lambda \mathbf{b}+3 \mathbf{c}, 3 \mathbf{a}+4 \mathbf{b}-\lambda \mathbf{c}$ and $\mathbf{a}-6 b+...

33Vector Algebra

A vector of magnitude $\sqrt{2}$ units along the internal bisector of the angle between the vectors $2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is

34Vector Algebra

$A(3,2,-1), B(4,1,0), C(2,1,4)$ are the vertices of a $\triangle A B C$. If the bisector of $B A C$ ! intersects the side $B C$ at $D(p, q, r)$, then $\sqrt{2 p+q+r}=$

35Vector Algebra

$r$ is a vector perpendicular to the planet, determined by the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$ and $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, If the magnitude of the projection of $\mathbf{r}$ on the vector $2 \hat{\mathbf{i}}+\ha...

36Vector Algebra

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If the three points $\lambda a-2 b+c, 2 a+\lambda b-2 \mathbf{c}$ and $4 \mathbf{a}+7 \mathbf{b}-8 \mathbf{c}$ are collinear, then $\lambda=$

37Vector Algebra

$\mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \mathbf{k}, \quad \mathbf{c}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are two vectors and $\mathbf{a}$ is a vector such that
$\cos (\mathbf{a}, \mathbf{b} \times \mathbf{c})=\sqrt...

38Vector Algebra

If $\mathrm{a}, \mathrm{b}$ are two vectors such that $|\mathrm{a}|=3,|\mathrm{~b}|=4$, $|\mathbf{a}+\mathbf{b}|=\sqrt{37},|\mathbf{a}-\mathbf{b}|=k$ and $(\mathbf{a}, \mathbf{b})=\theta$, then $\frac{4}{13}(k \sin \theta)^2=$

39Vector Algebra

$(3,0,2)$ and $(0,2, k)$ are the direction ratios of two lines and $\theta$ is the angle between them. If $|\cos \theta|=\frac{6}{13}$, then $k=$

40Vector Algebra

$2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ are the position vectores of two points $A$ and $B$ respectively and $C$ divides $A B$ in the ratio $3: 2$ : If $3 \hat{\m...

41Vector Algebra

$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \hat{\mathbf{b}}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{c}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ are three vectors. If $\hat...

42Vector Algebra

A unit vector $\hat{\mathbf{e}}=a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}$ is coplanar with the vectors $\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$, and $3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-5 \hat{\mathbf{k}}$. I...

43Vector Algebra

$P$ and $Q$ are the points of trisection of the segment $A B$. If $2 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $4 \hat{\mathbf{i}}+\hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ are the position vectors of $A$ and $B$ respectively, ...

44Vector Algebra

If $\mathbf{a}=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{b}=6 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are two vectors, then the magnitude of the component of $\mathbf{b}$ parallel to $\mathbf{a}$...

45Vector Algebra

$\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{c}=2 \hat{\mathbf{k}}-\hat{\mathbf{i}}$ are three vectors and $\mathbf{d}$ is a unit vector perpendicular to $\mathbf{c}$. If $\ma...

46Vector Algebra

The position vector of the point of intersection of the line joining the points $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and the line joining the points $2 \hat{\mathbf{i}}+\...

47Vector Algebra

If $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{c}=-\hat{\mathbf{k}}$ are position vectors of two points and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}, \mathbf{d}=\hat{\mathbf{i}}+...

48Vector Algebra

$\mathbf{a}$ is a vector perpendicular to the plane containing non zero vectors $\mathbf{b}$ and $\mathbf{c}$. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are such that$|\mathbf{a}+\mathbf{b}+\mathbf{c}|=\sqrt{|\mathbf{a}|^{2}+|\mathbf{b}|^{2}+...

49Vector Algebra

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors each having $\sqrt{2}$ magnitude such that $(\mathbf{a}, \mathbf{b})=(\mathbf{b}, \mathbf{c})=(\mathbf{c}, \mathbf{a})=\frac{\pi}{3}$. If $\mathbf{x}=\mathbf{a} \times(\mathbf{b} \times...

50Vector Algebra

If $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=3(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})$ and $\mathbf{c}$ is a vector such that $\mathbf{a} \times \mathbf{c}=\mathbf{b}$ and $\mathbf{a} . \mathb...