The value of i * (k x j) + j * (i x k) + k * (j x i) is Option 1: 0 Option 2: 3 Option 3: -1 Option 4: -3

Answer: -3. Solution: k x j = -i, so i * (-i) = -1. i x k = -j, so j * (-j) = -1. j x i = -k, so k * (-k) = -1. Sum = -3.

Algebra

Vector Algebra

Easy

The value of $\hat{i} \cdot (\hat{k} \times \hat{j}) + \hat{j} \cdot (\hat{i} \times \hat{k}) + \hat{k} \cdot (\hat{j} \times \hat{i})$ is

$0$

$3$

$-1$

$-3$

✅ Correct Option: 4

$\hat{k} \times \hat{j} = -\hat{i}$ , so $\hat{i} \cdot (-\hat{i}) = -1$ .

$\hat{i} \times \hat{k} = -\hat{j}$ , so $\hat{j} \cdot (-\hat{j}) = -1$ .

$\hat{j} \times \hat{i} = -\hat{k}$ , so $\hat{k} \cdot (-\hat{k}) = -1$ .

Sum $= -3$ .

2023: 22 May Shift 3

Match List - I with List - II.

	List - I		List - II
(A)	Area of triangle $\Delta$ with adjacent sides $\vec{a}$ and $\vec{b}$	(I)	$\vec{a} \times \vec{b}$
(B)	Area of parallelogram with adjacent sides $\vec{a}$ and $\vec{b}$	(II)	$\frac{1}{2}\lvert \vec{a} \times \vec{b} \rvert$
(C)	$(\vec{a} - \vec{b}) \times (\vec{a} + \vec{b})$	(III)	$\lvert \vec{a} \times \vec{b} \rvert$
(D)	$\lvert \vec{a} \rvert \lvert \vec{b} \rvert \sin\theta \hat{n}$ , where symbols have their usual meaning	(IV)	$2(\vec{a} \times \vec{b})$

Choose the correct answer from the options given below :

2026: 31 May Shift 2

If $|\vec{a}| = \sqrt{26}, |\vec{b}| = 7, |\vec{a}\times\vec{b}| = 35$ and $\theta$ be the angle between $\vec{a}$ and $\vec{b}$ then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\sin\theta$	I.	$61$
B.	$\cos\theta$	II.	$5/\sqrt{26}$
C.	$\vec{a} \cdot \vec{b}$	III.	$1/\sqrt{26}$
D.	$\vert \vec{a} - \vec{b} \vert^2$	IV.	$7$

Choose the correct answer from the options given below:

2025: 21 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The vectors $\lambda\hat{i}$ $+ \hat{j} + 2\hat{k}$ and $\vec{i} + \lambda\hat{j} + \hat{k}$ are perpendicular if λ is equal to	(I) 1
(B) The vectors $3\hat{i} + 6\hat{j} - \hat{k}$ and $2\hat{i} + 4\hat{j} - \lambda\hat{k}$ are collinear if λ is equal to	(II) -1
(C) The number of vectors of unit-length which are perpendicular to both the vectors $\vec{a}$ = $\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{b}$ = $3\hat{i} - \hat{j} + 5\hat{k}$ is	(III) 2/3
(D) If $\lvert \vec{a} \rvert = 1$ and $\vec{a} + \vec{b} = \vec{0}$ , then $\lvert \vec{b} \rvert$ is equal to	(IV) 2

Choose the correct answer from the options given below:

2025: 30 May Shift 1

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ and $|\vec{a}| = 5, |\vec{b}| = 3, |\vec{c}| = 7$ , then the acute angle between $\vec{a}$ and $\vec{b}$ is

2026: 26 May Shift 2

If $\vec{a} = 5\hat{i} - \hat{j} - 3\hat{k}$ and $\vec{b} = \hat{i} - 3\hat{j} - 5\hat{k}$ then $(\vec{a}+\vec{b}).(\vec{a}-\vec{b})$ is equal to:

2022: 16 July Shift 2

If $\theta$ is the acute angle between two unit vectors $\vec{a}$ and $\vec{b}$ , then $\cos\frac{\theta}{2} =$

The value of i^⋅(k^×j^)+j^⋅(i^×k^)+k^⋅(j^×i^)\hat{i} \cdot (\hat{k} \times \hat{j}) + \hat{j} \cdot (\hat{i} \times \hat{k}) + \hat{k} \cdot (\hat{j} \times \hat{i})i^⋅(k^×j^​)+j^​⋅(i^×k^)+k^⋅(j^​×i^) is

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\hat{i} \cdot (\hat{k} \times \hat{j}) + \hat{j} \cdot (\hat{i} \times \hat{k}) + \hat{k} \cdot (\hat{j} \times \hat{i})$ is