Vector Algebra PYQs - Last 10 Years

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Practice 31 COMEDK Mathematics questions from Vector Algebra. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

31

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Mathematics / Algebra

2020-2026

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25

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2022-2026

31

Last 10 Years

2017-2026

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31PYQs

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25 in last 5 years31 in last 10 years

Last 10 Years Vector Algebra Questions

Showing 31 of 31 filtered questions.

1Vector Algebra

Let $\vec{p}$ and $\vec{q}$ be the position vectors of P and Q with respect to the origin. If points R and S divide PQ internally and externally in the ratio 2:3 respectively, then $\overrightarrow{O R}$ and $\overrightarrow{O S}$ are perpe...

2Vector Algebra

\(\text { The direction ratios of the vector }(\hat{\imath}+\hat{\jmath}) \times(\hat{\jmath}+\hat{k}) \text { are }\)

3Vector Algebra

\(\text { If the projection of } \vec{a}=5 \hat{\imath}+\hat{\jmath}+\lambda \hat{k} \text { on } \vec{b}=2 \hat{\imath}+6 \hat{\jmath}+3 \hat{k} \text { is } 4 \text { units, then } \lambda=\)

4Vector Algebra

\(\text { If }(\vec{a}+\vec{b}) \perp \vec{b} \text { and }(\vec{a}+2 \vec{b}) \perp \vec{a} \text {, then }\)

5Vector Algebra

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $a \neq 0$ and $\vec{a} \times \vec{b}=2(\vec{a} \times \vec{c}),|\vec{a}|=|\vec{c}|=1,|\vec{b}|=4$ and $|\vec{b} \times \vec{c}|=\sqrt{15}$ if $\vec{b}-2 \vec{c}=\lambda \vec{a}$ t...

6Vector Algebra

A line $L_1$ passing through the point A with position vector $\vec{a}=4 \hat{i}+2 \hat{j}+2 \hat{k}$ is parallel to the vector $\vec{b}=2 \hat{i}+3 \hat{j}+6 \hat{k}$. The length of the perpendicular drawn from a point P with position vect...

7Vector Algebra

The magnitude of the projection of the vector $-\hat{\imath}+2 \hat{\jmath}-\hat{k}$ on the z -axis is

8Vector Algebra

For any vector $\vec{p}$, the value of $\left[2\left\{|\vec{p} \times \hat{\imath}|^2+|\vec{p} \times \hat{\jmath}|^2+|\vec{p} \times \hat{k}|^2\right\}\right]$ is

9Vector Algebra

If $\vec{a}$ and $\vec{b}$ are two vectors such that $\vec{a} \cdot \vec{b}=|\vec{a} \times \vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ is

10Vector Algebra

Position vector of P and Q are $\hat{\imath}+3 \hat{\jmath}-7 \hat{k}$ and $5 \hat{\imath}-2 \hat{\jmath}+4 \hat{k}$ respectively. Then the cosine of the angle between $\overrightarrow{P Q}$ and y -axis is

11Vector Algebra

If $|\vec{a}|=2 \sqrt{2}$ and $|\vec{b}|=3$ and angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$. If a parallelogram is constructed with adjacent sides $\vec{p}=2 \vec{a}-3 \vec{b}$ and $\vec{q}=\vec{a}+\vec{b}$ then the product of ...

12Vector Algebra

The vector \((\vec{r})\) whose magnitude is \(3 \sqrt{2}\) units which makes an angle of \(\frac{\pi}{4}\) and \(\frac{\pi}{2}\) with \(y\) and \(z\)- axis respectively is

13Vector Algebra

\(\text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|=\)

14Vector Algebra

Find the value of '\(b\)' such that the scalar product of the vector \(\hat{\imath}+\hat{\jmath}+\hat{k}\) with the unit vector parallel to the sum of the vectors \(2 \hat{\imath}+4 \hat{\jmath}-5 \hat{k}\) and $$b \hat{\imath}+2 \hat{\jmat...

15Vector Algebra

\(\text { If } \hat{\imath}+\hat{\jmath}-\hat{k} \quad \&~ 2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \text { are adjacent sides of a parallelogram, then length of its diagonals are }\)

16Vector Algebra

\(\text { The angle between } \hat{\imath}-\hat{\jmath} ~\&~ \hat{\jmath}-\hat{k} \text { is }\)

17Vector Algebra

Let a, b, c be three vector such that \(a \neq 0\) and \(\vec{a} \times \vec{b}=2 \vec{a} \times \vec{c},|a|=|c|=1,|b|=4\) and \(|\vec{b} \times \vec{c}|=\sqrt{15}\). If \(\vec{b}-2 \vec{c}=\lambda \vec{a}\) then \(\lambda\) equals to

18Vector Algebra

\(\text { If } \vec{a} \text { and } \vec{b} \text { are unit vectors, then the angle between } \vec{a} \text { and } \vec{b} \text { for which } a-\sqrt{2} \vec{b} \text { is a unit vector is }\)

19Vector Algebra

The scalar components of a unit vector which is perpendicular to each of the vectors \(\hat{\imath}+2 \hat{\jmath}-\hat{k}\) and \(3 \hat{\imath}-\hat{\jmath}+2 \hat{k}\) are

20Vector Algebra

\(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) and \(\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\), then unit vector parallel to $$\mathbf{a}+\mathbf{b}-...

21Vector Algebra

If the vectors \(\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=m \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are coplanar,...

22Vector Algebra

The angle between the vectors \(\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) is

23Vector Algebra

If \(\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}\) and \(\mathbf{r}=\hat{i}+\hat{k}\), then the unit vector in the direction of \(3 p+q-2 r\) is

24Vector Algebra

If x, y and z are non-zero real numbers and \(a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k\) and \(c = x\widehat i + y\widehat j + z\widehat k\) are such that \(a \times b = z\widehat i - 3\widehat j + \widehat k\), then [a b...

25Vector Algebra

If \(\theta\) be the angle between the vectors \(a = 2\widehat i + 2\widehat j - \widehat k\) and \(b = 6\widehat i - 3\widehat j + 2\widehat k\), then

26Vector Algebra

If for \(a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k\) and \(c = - 3\widehat i + \widehat j + 2\widehat k\), then find \([a\,b\,c]\).

27Vector Algebra

If |a| = 8, |b| = 3 and |a \(\times\) b| = 12, then find the angle between a and b.

28Vector Algebra

The vector that must be added to \(\widehat i - 3\widehat j + 2\widehat k\) and \(3\widehat i + 6\widehat j - 7\widehat k\) so resultant vector is a unit vector along the X-axis is

29Vector Algebra

OA and BO are two vectors of magnitudes 5 and 6 respectively. If \(\angle BOA=60^\circ\), then OA . OB is equal to

30Vector Algebra

If \(a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j - \widehat k\), then a vector perpendicular to a and in the plane containing b and c is

31Vector Algebra

If a and b are vectors such that \(|a + b|=|a-b|\), then the angle between a and b is