If = 4, = 3 and +b = 6, then -b = Option 1: √14 Option 2: 14 Option 3: 42 Option 4: 1

Answer: √14. Solution: Use, a+ b, ^2+, a- b, ^2 = 2(, a, ^2+, b, ^2). So 36+, a- b, ^2 = 2(16+9)=50, giving, a- b, ^2=14 and, a- b, =√14.

Algebra

Vector Algebra

Easy

core

If $\lvert\vec{a}\rvert = 4, \lvert\vec{b}\rvert = 3$ and $\lvert\vec{a}+\vec{b}\rvert = 6$ , then $\lvert\vec{a}-\vec{b}\rvert =$

$\sqrt{14}$

$4\sqrt2$

✅ Correct Option: 1

Use $|\vec a+\vec b|^2+|\vec a-\vec b|^2 = 2(|\vec a|^2+|\vec b|^2)$ .

So $36+|\vec a-\vec b|^2 = 2(16+9)=50$ , giving $|\vec a-\vec b|^2=14$ and $|\vec a-\vec b|=\sqrt{14}$ .

2025: 14 May Shift 2

If $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ , then which of the following statements is/are correct?

(A) $\vec{a}$ and $\vec{b}$ are collinear

(B) $\vec{a}$ and $\vec{b}$ are perpendicular

(D) $|\vec{a} + \vec{b}| = 2\sqrt{5}$

Choose the correct answer from the options given below:

2025: 15 May Shift 1

If $\vec{a} = 2\hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = 2\hat{i} + 2\hat{j} + \hat{k}$ , then

Match List-I with List-II

List-I	List-II
(A) Projection of $\vec{a}$ on $\vec{b}$ is	(I) $-7\hat{i} + 4\hat{j} + 6\hat{k}$
(B) $\vec{a} \times \vec{b}$ is	(II) $\frac{1}{\sqrt{101}}(-7\hat{i} + 4\hat{j} + 6\hat{k})$
(C) unit vector along $\vec{a} + \vec{b}$ is	(III) $\frac{5}{3}$
(D) Unit vector perpendicular to both $\vec{a}$ & $\vec{b}$ is	(IV) $\frac{1}{\sqrt{33}}(4\hat{i} + \hat{j} + 4\hat{k})$

Choose the correct answer from the options given below:

2025: 19 May Shift 1

Match List-I with List-II

List-I	List-II
Mathematical Statement	Value
(A) $\hat{i} \cdot (\hat{j} \times \hat{k})$	(I) $-\hat{k}$
(B) $\hat{j} \cdot (\hat{i} \times \hat{k})$	(II) 1
(C) $\hat{i} \times (\hat{j} \times \hat{k})$	(III) -1
(D) $\hat{j} \times \hat{i}$	(IV) $\vec{0}$

Choose the correct answer from the options given below:

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

2026: 19 May Shift 2

Let $\vec{a}$ and $\vec{b}$ be two vectors, such that $|\vec{a}| = 3, |\vec{b}| = 5$ and the angle between them is $60°$ , then the value of $|\vec{a} + \vec{b}|$ is

2022: 25 May Shift 1

Let the vectors $\vec{a} = \hat{i} - 3\hat{j} + 2\hat{k}, \vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{c} = 3\hat{i} + 5\hat{j} - 2\lambda\hat{k}$ be coplanar. Then $\lambda$ is equal to

If ∣a⃗∣=4,∣b⃗∣=3\lvert\vec{a}\rvert = 4, \lvert\vec{b}\rvert = 3∣a∣=4,∣b∣=3 and ∣a⃗+b⃗∣=6\lvert\vec{a}+\vec{b}\rvert = 6∣a+b∣=6, then ∣a⃗−b⃗∣=\lvert\vec{a}-\vec{b}\rvert =∣a−b∣=

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\lvert\vec{a}\rvert = 4, \lvert\vec{b}\rvert = 3$ and $\lvert\vec{a}+\vec{b}\rvert = 6$ , then $\lvert\vec{a}-\vec{b}\rvert =$