Let a = i + j + k and b = i + 2j + 3k then a unit vector perpendicular to both vectors (a + b) and (a - b) is equal to Option 1: 1/√6(-i + 2j - k) Option 2: 1/√6(i - 2j - k) Option 3: 1/√3(i + j + k) Option 4: 1/√6(i + 2j + k)

Answer: 1/√6(-i + 2j - k). Solution: Solution Coming Soon

Algebra

Vector Algebra

Medium

core

Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + \hat{2j} + 3\hat{k}$ then a unit vector perpendicular to both vectors $(\vec{a} + \vec{b})$ and $(\vec{a} - \vec{b})$ is equal to

$\frac{1}{\sqrt{6}}(-\hat{i} + 2\hat{j} - \hat{k})$

$\frac{1}{\sqrt{6}}(\hat{i} - 2\hat{j} - \hat{k})$

$\frac{1}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k})$

$\frac{1}{\sqrt{6}}(\hat{i} + 2\hat{j} + \hat{k})$

✅ Correct Option: 1

Solution Coming Soon

2025: 14 May Shift 2

Let $\vec{a} = \hat{i} + \hat{j}$ , $\vec{b} = \hat{i} - \hat{j}$ and $\vec{c} = \hat{i} + \hat{j} + \hat{k}$ . If $\hat{m}$ is a unit vector perpendicular to both $\vec{a}$ and $\vec{b}$ , then $|\vec{c}.\hat{m}|$ is equal to

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) The value of $\hat{i}\cdot(\hat{j}\times\hat{k}) + \hat{j}\cdot(\hat{i}\times\hat{k}) + \hat{k}\cdot(\hat{i}\times\hat{j})$	(I) 16
(B) If $\lvert\vec{a}\rvert=10$ , $\lvert\vec{b}\rvert=2$ and $\vec{a}\cdot\vec{b}=12$ , then the value of $\lvert\vec{a}\times\vec{b}\rvert$ is	(II) $\frac{\pi}{4}$
(C) If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b}$ , then the value of $\theta$ , for which $\vec{a}\cdot\vec{b} = \lvert\vec{a}\times\vec{b}\rvert$ is	(III) 14
(D) If $\vec{a}$ and $\vec{b}$ are perpendicular and $\vec{a} = 2\hat{i}+4\hat{j}+\lambda\hat{k}$ and $\vec{b} = 3\hat{i}-5\hat{j}+\hat{k}$ , then the value of $\lambda$ is	(IV) 1

Choose the correct answer from the options given below :

2026: 19 May Shift 2

If $\theta$ is angle between $\vec{a}$ & $\vec{b}$ , then for vectors $\vec{a}, \vec{b}$ and $\vec{c}$ ,

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vec{a} \times \vec{b} = \vec{a} \times \vec{c}, \vec{a} \neq 0, \vec{b} \neq \vec{c}$	I.	$\theta = \dfrac{\pi}{4}$
B.	$\vec{a} \times \vec{b} = 0$	II.	$\vec{a} \parallel (\vec{b} - \vec{c})$
C.	$\vert \vec{a}.\vec{b} \vert = \vert \vec{a} \times \vec{b} \vert$	III.	$\vec{b} = \vec{c}$
D.	$\vec{a}.\vec{b} = \vec{a}.\vec{c}$ and $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ , $\vec{a} \neq 0$	IV.	$\vec{a} = 0, \vec{b} = 0$ or $\vec{a} \parallel \vec{b}$

Choose the correct answer from the options given below:

2025: 2 June Shift 1

If A (3, 2), B (1, -1) and C (2, 1) are three vertices of a parallelograms ABCD, then its area (in sq.units) is equal to

2026: 29 May Shift 1

If the angle between the vectors $\vec a=2\lambda^2\hat i+4\lambda\hat j+\hat k$ and $\vec b=7\hat i-2\hat j+\lambda\hat k$ is obtuse, then

2026: 18 May Shift 2

If $P(\vec{r})$ is a position vector of a point with scalar components $(x,y,z)$ , then the value of $(\vec{r}.\hat{i})(-\hat{i})-(\vec{r}.\hat{j})\hat{j}+(\vec{r}.(-\hat{k}))\hat{k}$ , is:

Let a⃗=i^+j^+k^\vec{a} = \hat{i} + \hat{j} + \hat{k}a=i^+j^​+k^ and b⃗=i^+2j^+3k^\vec{b} = \hat{i} + \hat{2j} + 3\hat{k}b=i^+2j^​+3k^ then a unit vector perpendicular to both vectors (a⃗+b⃗)(\vec{a} + \vec{b})(a+b) and (a⃗−b⃗)(\vec{a} - \vec{b})(a−b) is equal to

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CUET Mathematics Past Year Questions (Topic-Wise)

Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + \hat{2j} + 3\hat{k}$ then a unit vector perpendicular to both vectors $(\vec{a} + \vec{b})$ and $(\vec{a} - \vec{b})$ is equal to