VITEEE PYQs for Vector Algebra with Solutions: Practice VITEEE Previous Year Questions

Updated 3+ months ago

Vector Algebra is an important topic in the Mathematics section in VITEEE exam. Practising this topic will increase your score overall and make your conceptual grip on VITEEE exam stronger.

This article gives you a full set of VITEEE PYQs for Vector Algebra with explanations for effective preparation. Practice of VITEEE Mathematics PYQs including Vector Algebra questions regularly will improve accuracy, speed, and confidence in the VITEEE 2026 exam.

VITEEE PYQs for Vector Algebra with Solutions

1.
The length of longer diagonal of the parallelogram constructed on $ 5a + 2b $ and $ a - 3b $, if it is given that $ |a| = 2\sqrt{2} $, $ |b| = 3 $, and the angle between $ a $ and $ b $ is $ \frac{\pi}{4} $, is?
- $ \sqrt{593} $
- $ \sqrt{113} $
- $ \sqrt{369} $
- $ \sqrt{563} $
View Solution
2.
If vector equation of the line$\frac{x-2}{2}=\frac{2y-5}{-3}=z+1,$ is $\vec{r}=\left(2\hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2\hat{i}-\frac{3}{2} \hat{j}+p\hat{k}\right)$ then $p$ is equal to
- $0$
- $1$
- $2$
- $3$
View Solution
3.
If the equations $ x + ay = 0 $, $ 2x + y + az = 0 $, $ ax + y + 2z = 0 $ have non-trivial solutions, then $ a = $:
- 2
- -2
- $ \sqrt{3} $
- $ -\sqrt{3} $
View Solution
4.
If $\left(\vec{a}\times\vec{b}\right)^{2}+\left(\vec{a}.\vec{b}\right)^{2}=676$ and $\left|\vec{b}\right|=2,$ then $\left|\vec{a}\right|$ is equal to
- $13$
- $26$
- $39$
- None of these
View Solution
5.
If $\vec {a} = \hat {i} + \hat{j} + \hat{k}$, $\vec {b} = \vec {i} + 3\vec {j} + 5\hat{k}$ and $\vec {c} = 7\hat{i} + 9\hat {j} + 11 \hat{k}$, then the area of Parallelogram having diagonals $\vec{a} +\vec{b}$ and $\vec{b} +\vec{c}$ is
- $4 \sqrt{6}$ s units
- $\frac{1}{2} \sqrt{21}$ s units
- $48$
- $ \sqrt{6}$ s units
View Solution
6.
If $m_{1}, m_{2}, m_{3}$ and $m_{4}$ are respectively the magnitudes of the vectors $\vec{ a }_{1}=2 \hat{ i }-\hat{ j }+\hat{ k }, \,\,\,\vec{ a }_{2}=3 \hat{ i }-4 \hat{ j }-4 \hat{ k }$ $\vec{ a }_{3}=\hat{ i }+\hat{ j }-\hat{ k } \,\,\,$ and $\,\,\,\vec{ a }_{4}=-\hat{ i }+3 \hat{ j }+\hat{ k }$ then the correct order of $m_{1}, m_{2}, m_{3}$ and $m_{4}$ is
- $m_3 < m_1 < m_4 < m_2$
- $m_3 < m_1 < m_2 < m_4$
- $m_3 < m_4 < m_1 < m_2$
- $m_3 < m_4 < m_2 < m_1$
View Solution
7.
The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to
- $\frac{3}{2}\left(\vec {i}+\vec {j}\right)$
- $\frac{2}{3}\left(\vec{i}+\vec{j}\right)$
- $\frac{1}{2}\left(\vec {i}+\vec{j}\right)$
- $\frac{1}{3}\left(\vec {i}+\vec {j}\right)$
View Solution
8.
A unit vector perpendicular to the plane formed by the points $ (1, 0, 1) $, $ (0, 2, 2) $, and $ (3, 3, 0) $ is:
- $ \frac{1}{\sqrt{5}} (5\hat{i} - \hat{j} - 7\hat{k}) $
- $ \frac{1}{\sqrt{3}} (5\hat{i} + 7\hat{k}) $
- $ \frac{1}{\sqrt{3}} (5\hat{i} + 7\hat{j} + 7\hat{k}) $
- None of these
View Solution
9.
What is the length of the projection of $ 3\hat{i} + 4\hat{j} + 5\hat{k} $ on the xy-plane?
- 3
- 5
- 7
- 9
View Solution
10.
If $ \mathbf{a} = ( \hat{i} + \hat{j} + \hat{k} ) $, $ \mathbf{a} \times \mathbf{b} = \hat{i} - \hat{j} $, then $ \mathbf{b} $ is:
- $ \hat{i} + 2\hat{k} $
- $ 2\hat{i} + 2\hat{k} $
- $ 2\hat{i} - 2\hat{k} $
- $ 2\hat{i} + 2\hat{j} $
View Solution
11.
If $ r = a \times b \times c + \beta \cdot a + \gamma \cdot b + [a \, b \, c] = 2 $, then $ a + \beta + \gamma $ is equal to?
- $ [b \cdot c + a \times b] $
- $ \frac{1}{2} (a + b + c) $
- $ 2a + b + c $
- None of these
View Solution
12.
The position vector of $A$ and $B$ are $ 2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$ The length of the internal bisector of $?BOA$ triangle $AOB$ is
- $\sqrt{\frac{136}{9}}$
- $\frac{\sqrt{136}}{9}$
- $\sqrt{\frac{217}{9}}$
- $\frac{20}{3}$
View Solution
13.
If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to
- $ l + m + n $
- $l^3 + m^3 + n^3$
- $l^2 + m^2 + n^2 $
- None of these
View Solution
14.
If the system of equations \[ x + ky - z = 0, \quad 3x - ky - z = 0, \quad x - 3y + z = 0, \] has a non-zero solution, then $ k $ is equal to:
- $ -1 $
- $ 0 $
- $ 1 $
- $ 2 $
View Solution
15.
If $ a $, $ b $, and $ c $ are three non-coplanar vectors and $ p, q, r $ are reciprocal vectors, then $ (p + q + r) $ is equal to?
- $ (p^3 + m^3 + n^3) $
- $ [r + p + q] $
- $ p^3 + q^3 + r^3 $
- None of these
View Solution

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VITEEE PYQs for Vector Algebra with Solutions: Practice VITEEE Previous Year Questions

VITEEE PYQs for Vector Algebra with Solutions

1.
The length of longer diagonal of the parallelogram constructed on \( 5a + 2b \) and \( a - 3b \), if it is given that \( |a| = 2\sqrt{2} \), \( |b| = 3 \), and the angle between \( a \) and \( b \) is \( \frac{\pi}{4} \), is?

2.
If vector equation of the line$\frac{x-2}{2}=\frac{2y-5}{-3}=z+1,$ is $\vec{r}=\left(2\hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2\hat{i}-\frac{3}{2} \hat{j}+p\hat{k}\right)$ then $p$ is equal to

3.
If the equations \( x + ay = 0 \), \( 2x + y + az = 0 \), \( ax + y + 2z = 0 \) have non-trivial solutions, then \( a = \):

4.
If $\left(\vec{a}\times\vec{b}\right)^{2}+\left(\vec{a}.\vec{b}\right)^{2}=676$ and $\left|\vec{b}\right|=2,$ then $\left|\vec{a}\right|$ is equal to

5.
If $\vec {a} = \hat {i} + \hat{j} + \hat{k}$, $\vec {b} = \vec {i} + 3\vec {j} + 5\hat{k}$ and $\vec {c} = 7\hat{i} + 9\hat {j} + 11 \hat{k}$, then the area of Parallelogram having diagonals $\vec{a} +\vec{b}$ and $\vec{b} +\vec{c}$ is

7.
The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to

8.
A unit vector perpendicular to the plane formed by the points \( (1, 0, 1) \), \( (0, 2, 2) \), and \( (3, 3, 0) \) is:

9.
What is the length of the projection of \( 3\hat{i} + 4\hat{j} + 5\hat{k} \) on the xy-plane?

10.
If \( \mathbf{a} = ( \hat{i} + \hat{j} + \hat{k} ) \), \( \mathbf{a} \times \mathbf{b} = \hat{i} - \hat{j} \), then \( \mathbf{b} \) is:

11.
If \( r = a \times b \times c + \beta \cdot a + \gamma \cdot b + [a \, b \, c] = 2 \), then \( a + \beta + \gamma \) is equal to?

12.
The position vector of $A$ and $B$ are $ 2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$ The length of the internal bisector of $?BOA$ triangle $AOB$ is

13.
If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to

14.
If the system of equations \[ x + ky - z = 0, \quad 3x - ky - z = 0, \quad x - 3y + z = 0, \] has a non-zero solution, then \( k \) is equal to:

15.
If \( a \), \( b \), and \( c \) are three non-coplanar vectors and \( p, q, r \) are reciprocal vectors, then \( (p + q + r) \) is equal to?

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VITEEE PYQs for Vector Algebra with Solutions

1.The length of longer diagonal of the parallelogram constructed on \( 5a + 2b \) and \( a - 3b \), if it is given that \( |a| = 2\sqrt{2} \), \( |b| = 3 \), and the angle between \( a \) and \( b \) is \( \frac{\pi}{4} \), is?

2.If vector equation of the line$\frac{x-2}{2}=\frac{2y-5}{-3}=z+1,$ is $\vec{r}=\left(2\hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2\hat{i}-\frac{3}{2} \hat{j}+p\hat{k}\right)$ then $p$ is equal to

3.If the equations \( x + ay = 0 \), \( 2x + y + az = 0 \), \( ax + y + 2z = 0 \) have non-trivial solutions, then \( a = \):

4.If $\left(\vec{a}\times\vec{b}\right)^{2}+\left(\vec{a}.\vec{b}\right)^{2}=676$ and $\left|\vec{b}\right|=2,$ then $\left|\vec{a}\right|$ is equal to

5.If $\vec {a} = \hat {i} + \hat{j} + \hat{k}$, $\vec {b} = \vec {i} + 3\vec {j} + 5\hat{k}$ and $\vec {c} = 7\hat{i} + 9\hat {j} + 11 \hat{k}$, then the area of Parallelogram having diagonals $\vec{a} +\vec{b}$ and $\vec{b} +\vec{c}$ is

7.The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to

8.A unit vector perpendicular to the plane formed by the points \( (1, 0, 1) \), \( (0, 2, 2) \), and \( (3, 3, 0) \) is:

9.What is the length of the projection of \( 3\hat{i} + 4\hat{j} + 5\hat{k} \) on the xy-plane?

10.If \( \mathbf{a} = ( \hat{i} + \hat{j} + \hat{k} ) \), \( \mathbf{a} \times \mathbf{b} = \hat{i} - \hat{j} \), then \( \mathbf{b} \) is:

11.If \( r = a \times b \times c + \beta \cdot a + \gamma \cdot b + [a \, b \, c] = 2 \), then \( a + \beta + \gamma \) is equal to?

12.The position vector of $A$ and $B$ are $ 2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$ The length of the internal bisector of $?BOA$ triangle $AOB$ is

13.If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to

14.If the system of equations \[ x + ky - z = 0, \quad 3x - ky - z = 0, \quad x - 3y + z = 0, \] has a non-zero solution, then \( k \) is equal to:

15.If \( a \), \( b \), and \( c \) are three non-coplanar vectors and \( p, q, r \) are reciprocal vectors, then \( (p + q + r) \) is equal to?

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1.
The length of longer diagonal of the parallelogram constructed on \( 5a + 2b \) and \( a - 3b \), if it is given that \( |a| = 2\sqrt{2} \), \( |b| = 3 \), and the angle between \( a \) and \( b \) is \( \frac{\pi}{4} \), is?

2.
If vector equation of the line$\frac{x-2}{2}=\frac{2y-5}{-3}=z+1,$ is $\vec{r}=\left(2\hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2\hat{i}-\frac{3}{2} \hat{j}+p\hat{k}\right)$ then $p$ is equal to

3.
If the equations \( x + ay = 0 \), \( 2x + y + az = 0 \), \( ax + y + 2z = 0 \) have non-trivial solutions, then \( a = \):

4.
If $\left(\vec{a}\times\vec{b}\right)^{2}+\left(\vec{a}.\vec{b}\right)^{2}=676$ and $\left|\vec{b}\right|=2,$ then $\left|\vec{a}\right|$ is equal to

5.
If $\vec {a} = \hat {i} + \hat{j} + \hat{k}$, $\vec {b} = \vec {i} + 3\vec {j} + 5\hat{k}$ and $\vec {c} = 7\hat{i} + 9\hat {j} + 11 \hat{k}$, then the area of Parallelogram having diagonals $\vec{a} +\vec{b}$ and $\vec{b} +\vec{c}$ is

7.
The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to

8.
A unit vector perpendicular to the plane formed by the points \( (1, 0, 1) \), \( (0, 2, 2) \), and \( (3, 3, 0) \) is:

9.
What is the length of the projection of \( 3\hat{i} + 4\hat{j} + 5\hat{k} \) on the xy-plane?

10.
If \( \mathbf{a} = ( \hat{i} + \hat{j} + \hat{k} ) \), \( \mathbf{a} \times \mathbf{b} = \hat{i} - \hat{j} \), then \( \mathbf{b} \) is:

11.
If \( r = a \times b \times c + \beta \cdot a + \gamma \cdot b + [a \, b \, c] = 2 \), then \( a + \beta + \gamma \) is equal to?

12.
The position vector of $A$ and $B$ are $ 2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$ The length of the internal bisector of $?BOA$ triangle $AOB$ is

13.
If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to

14.
If the system of equations \[ x + ky - z = 0, \quad 3x - ky - z = 0, \quad x - 3y + z = 0, \] has a non-zero solution, then \( k \) is equal to:

15.
If \( a \), \( b \), and \( c \) are three non-coplanar vectors and \( p, q, r \) are reciprocal vectors, then \( (p + q + r) \) is equal to?