A vector of magnitude 9, which is perpendicular to both the vectors 4i-j+3k and -2i+j-2k is: Option 1: -3i+6j+6k Option 2: -3i-6j+6k Option 3: 3i-6j+6k Option 4: 3i+6j-6k

Answer: -3i+6j+6k. Solution: The cross product is (4,-1,3)x(-2,1,-2)=(2-3, -(-8+6), 4-2)=(-1,2,2). Its magnitude is 3, so the unit normal is 13(- i+2 j+2 k). Multiplying by 9 gives -3 i+6 j+6 k.

Algebra

Vector Algebra

Easy

core

A vector of magnitude 9, which is perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

$-3\hat{i}+6\hat{j}+6\hat{k}$

$-3\hat{i}-6\hat{j}+6\hat{k}$

$3\hat{i}-6\hat{j}+6\hat{k}$

$3\hat{i}+6\hat{j}-6\hat{k}$

✅ Correct Option: 1

The cross product is $(4,-1,3)\times(-2,1,-2)=(2-3,\,-(-8+6),\,4-2)=(-1,2,2)$ .

Its magnitude is $3$ , so the unit normal is $\frac13(-\hat i+2\hat j+2\hat k)$ .

Multiplying by $9$ gives $-3\hat i+6\hat j+6\hat k$ .

2026: 21 May Shift 2

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}| = 2, |\vec{b}| = 5, |\vec{c}| = 3$ and $\vec{a} + 2\vec{b} - 3\vec{c} = \vec{0}$ , then angle between $\vec{b}$ and $\vec{c}$ is equal to:

2026: 25 May Shift 1

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Area of triangle determined by vectors $(\hat{i}+\hat{j})$ and $(\hat{i}-2\hat{j}+\hat{k})$ is	I. 0
B. The value of $(\hat{i}\times\hat{j}).\hat{j} + (\hat{j}\times\hat{i}).\hat{k} + (\hat{k}\times\hat{i}).\hat{j}$ is	II. $\dfrac{\sqrt{11}}{2}$
C. If $(2\lambda-1)\hat{i}+3\hat{j}-\hat{k}$ and $\hat{i}+\lambda\hat{j}+2\hat{k}$ are perpendicular to each other then $\lambda$ is	III. 4
D. Projection of $5\hat{i}+\hat{j}+4\hat{k}$ on $2\hat{i}+6\hat{j}+3\hat{k}$ is	IV. 3/5

Choose the correct answer from the options given below:

2025: 3 June Shift 2

Let $\theta$ be the angle between two vectors $\vec{a}$ and $\vec{b}$ . Then match List-I with List-II

List-I	List-II
(A) $\sin \theta$	(I) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{a}\vert \vert \vec{b}\vert }$
(B) $\cos \theta$	(II) $\vert \vec{a} \times \vec{b}\vert$
(C) Area of the parallelogram with adjacent sides represented by $\vec{a}$ and $\vec{b}$	(III) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{a}\vert }$
(D) Projection of $\vec{a}$ on $\vec{b}$	(IV) $\dfrac{\vert \vec{a} \times \vec{b}\vert }{\vert \vec{a}\vert \vert \vec{b}\vert }$

Choose the correct answer from the options given below:

2024: 16 May Shift 1

If $(\vec{a}-\vec{b}) \cdot(\vec{a}+\vec{b})=27$ and $|\vec{a}|=2|\vec{b}|$ , then $|\vec{b}|$ is :

2026: 22 May Shift 2

A unit vector perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

2026: 21 May Shift 2

Let $\vec{a}$ and $\vec{b}$ be any two vectors such that $\vec{a} = 2\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = 3\hat{i} + 5\hat{j} - 2\hat{k}$ then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert \vec{a} \vert$	I.	$5$
B.	$\vert \vec{b} \vert$	II.	$\sqrt{507}$
C.	$\vert \vec{a}.\vec{b} \vert$	III.	$\sqrt{38}$
D.	$\vert \vec{a} \times \vec{b} \vert$	IV.	$\sqrt{14}$

Choose the correct answer from the options given below:

A vector of magnitude 9, which is perpendicular to both the vectors 4i^−j^+3k^4\hat{i}-\hat{j}+3\hat{k}4i^−j^​+3k^ and −2i^+j^−2k^-2\hat{i}+\hat{j}-2\hat{k}−2i^+j^​−2k^ is:

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CUET Mathematics Past Year Questions (Topic-Wise)

A vector of magnitude 9, which is perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is: