The area of the parallelogram determined by the vectors i + 2j + 3k and 3i - 2j + k is Option 1: 8√3 Option 2: 4√3 Option 3: 16√3 Option 4: 2√3

Answer: 8√3. Solution: a x b = (1,2,3) x (3,-2,1) = (2 * 1 - 3 * (-2), 3 * 3 - 1 * 1, 1 * (-2) - 2 * 3) = (8, 8, -8). Magnitude = √(64+64+64) = 8√3.

Algebra

Vector Algebra

Easy

core

The area of the parallelogram determined by the vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $3\hat{i} - 2\hat{j} + \hat{k}$ is

$8\sqrt{3}$

$4\sqrt{3}$

$16\sqrt{3}$

$2\sqrt{3}$

✅ Correct Option: 1

$\vec{a} \times \vec{b} = (1,2,3) \times (3,-2,1) = (2 \cdot 1 - 3 \cdot (-2), 3 \cdot 3 - 1 \cdot 1, 1 \cdot (-2) - 2 \cdot 3) = (8, 8, -8)$ . Magnitude $= \sqrt{64+64+64} = 8\sqrt{3}$ .

2026: 15 May Shift 1

If $|\vec a|=2, |\vec b|=7, \vec a \times \vec b = 3\hat i + 2\hat j + 6\hat k$ , then the angle between $\vec a$ and $\vec b$ is equal to

2026: 25 May Shift 1

If $\lvert\vec{a}\rvert = \lvert\vec{b}\rvert = \lvert\vec{a}+\vec{b}\rvert = 1$ , then

Match List-I with List-II

LIST-I	LIST-II
A. $\lvert\vec{a}-\vec{b}\rvert$	I. $\dfrac{2\pi}{3}$
B. Angle between $\vec{a}$ and $\vec{b}$	II. $-\dfrac{1}{2}$
C. Angle between $\vec{a}$ and $\vec{a}+\vec{b}$	III. $\sqrt3$
D. $\vec{a}.\vec{b}$	IV. $\dfrac{\pi}{3}$

Choose the correct answer from the options given below:

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) If vector $\vec{a}$ and $\vec{b}$ are such that $\vec{a} = \lambda \vec{b}$ and $\vert \vec{a}\vert = \vert \vec{b}\vert$ , then	(I) $\vec{a}$ and $\vec{b}$ are orthogonal
(B) Projection vector of $\vec{a}$ on $\vec{b}$	(II) $[0, 12]$
(C) $\vec{a}$ and $\vec{b}$ are non-zero vectors such that $\vert \vec{a} + \vec{b}\vert = \vert \vec{a} - \vec{b}\vert$ , then	(III) $\vec{a} = \pm \vec{b}$
(D) If $\vert \vec{a}\vert = 4, -3 \le \lambda \le 2$ , then the range of $\vert \lambda \vec{a}\vert$	(IV) $(\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{b}\vert ^2}) \vec{b}$

Choose the correct answer from the options given below:

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:

2025: 21 May Shift 2

The area of triangle with vertices P, Q, R is given by (where $\vec{AB}$ = position vector of point B – position vector of point A)

2025: 21 May Shift 1

If $\vec{a}$ , $\vec{b}$ and $\sqrt{3}\vec{a} - \vec{b}$ are three unit vectors, then the angle between $\vec{a}$ and $\vec{b}$ is:

The area of the parallelogram determined by the vectors i^+2j^+3k^\hat{i} + 2\hat{j} + 3\hat{k}i^+2j^​+3k^ and 3i^−2j^+k^3\hat{i} - 2\hat{j} + \hat{k}3i^−2j^​+k^ is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The area of the parallelogram determined by the vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $3\hat{i} - 2\hat{j} + \hat{k}$ is