If i, j, k represents unit vectors along x, y, z axes respectively, then Match List-I with List-II, LIST-I, LIST-II, A., i.i, I. 0, B., i.j, II. 0, C., i x j, III. 1, D., i x i, IV. k, Choose the correct answer from the options given below: Option 1: A-I, B-IV, C-II, D-III Option 2: A-II, B-III, C-IV, D-I Option 3: A-III, B-IV, C-II, D-I Option 4: A-III, B-I, C-IV, D-II

Answer: A-III, B-I, C-IV, D-II. Solution: ii = 1 (III) since the vectors are unit and parallel. ij = 0, a scalar (I), as they are perpendicular. ixj = k (IV) by the right-hand rule. ixi = 0, the zero vector (II).

Algebra

Vector Algebra

Easy

core

If $\hat{i}, \hat{j}, \hat{k}$ represents unit vectors along x, y, z axes respectively, then

Match List-I with List-II

LIST-I LIST-II
A. $\hat{i}.\hat{i}$ I. 0
B. $\hat{i}.\hat{j}$ II. $\vec{0}$
C. $\hat{i} \times \hat{j}$ III. 1
D. $\hat{i} \times \hat{i}$ IV. $\hat{k}$

Choose the correct answer from the options given below:

LIST-I		LIST-II
A.	$\hat{i}.\hat{i}$	I. 0
B.	$\hat{i}.\hat{j}$	II. $\vec{0}$
C.	$\hat{i} \times \hat{j}$	III. 1
D.	$\hat{i} \times \hat{i}$	IV. $\hat{k}$

A-I, B-IV, C-II, D-III

A-II, B-III, C-IV, D-I

A-III, B-IV, C-II, D-I

A-III, B-I, C-IV, D-II

✅ Correct Option: 4

$\hat{i}\cdot\hat{i} = 1$ (III) since the vectors are unit and parallel.

$\hat{i}\cdot\hat{j} = 0$ , a scalar (I), as they are perpendicular.

$\hat{i}\times\hat{j} = \hat{k}$ (IV) by the right-hand rule.

$\hat{i}\times\hat{i} = \vec{0}$ , the zero vector (II).

2026: 31 May Shift 2

In $\triangle ABC$ , Which of the following are True?

A. $\overline{AB}+\overline{BC}+\overline{CA}=\vec{0}$

B. $\overline{AB}+\overline{BC}-\overline{AC}=\vec{0}$

C. $\overline{AB}+\overline{BC}-\overline{CA}=\vec{0}$

D. $\overline{AB}-\overline{CB}+\overline{CA}=\vec{0}$

Choose the correct answer from the options given below:

2026: 21 May Shift 1

Let $\vec{a}$ be any vector such that $\vec{a}.\hat{i} = \vec{a}.(\hat{i}+\hat{j}) = \vec{a}.(\hat{i}+\hat{j}+\hat{k}) = 1$ , then $\vec{a}$ is

2022: 23 Aug Shift 1

A vector perpendicular to a plane containing a triangle ABC having vertices as $A(1,1,0)$ , $B(2,1,1)$ and $C(0,3,2)$ , is:

2025: 13 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Angle between $\vec{i} - \vec{j}$ and $\vec{j} + \vec{k}$	(I) 0
(B) Angle between $2\vec{j} - \vec{k}$ and $\vec{j} + 2\vec{k}$	(II) $\frac{2\pi}{3}$
(C) Angle between $\vec{i} + 2\vec{j}$ and $5\vec{i} + 10\vec{j}$	(III) $\frac{\pi}{6}$
(D) Angle between $\sqrt{3}\vec{i} + \vec{j}$ and $\vec{i}$	(IV) $\frac{\pi}{2}$

Choose the correct answer from the options given below:

2023: 22 May Shift 3

The position vector of a point R which divides the line joining two points P and Q whose position vectors are $\hat{i} + 2\hat{j} - \hat{k}$ and $-\hat{i} + \hat{j} + \hat{k}$ respectively in the ratio 2 : 1 externally is :

2025: 14 May Shift 1

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

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