If a, b, c are unit vectors such that a + b + c = 0. The value of a.b + b.c + c.a is Option 1: -3/2 Option 2: 3/2 Option 3: -1/2 Option 4: 1/2

Answer: -3/2. Solution: Square the given relation:, a+ b+ c, ^2=, a, ^2+, b, ^2+, c, ^2+2( a* b+ b* c+ c* a)=0. With unit vectors this is 3+2S=0, so S=-32.

Algebra

Vector Algebra

Easy

core

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$ . The value of $\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}$ is

$-\frac{3}{2}$

$\frac{3}{2}$

$-\frac{1}{2}$

$\frac{1}{2}$

✅ Correct Option: 1

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:

2026: 21 May Shift 2

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}| = 2, |\vec{b}| = 5, |\vec{c}| = 3$ and $\vec{a} + 2\vec{b} - 3\vec{c} = \vec{0}$ , then angle between $\vec{b}$ and $\vec{c}$ is equal to:

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

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) $(\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{b}\vert ^2}) \vec{b}$

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2026: 19 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $(\vec{a}-\vec{b}) \times (\vec{a}+\vec{b})$ equals	(I) $\vec{0}$
(B) $\vec{a} = (3\hat{i}+\hat{j}-4\hat{k}), \vec{b} = (6\hat{i}+5\hat{j}-2\hat{k})$ , then $\left\vert \vec{a}\times\vec{b} \right\vert$ equals	(II) $5$
(C) $\vec{a}\times(\vec{b}+\vec{c}) + \vec{b}\times(\vec{c}+\vec{a}) + \vec{c}\times(\vec{a}+\vec{b}) =$	(III) $2(\vec{a}\times\vec{b})$
(D) Projection of vector $(\hat{i}+3\hat{j}+7\hat{k})$ on vector $(2\hat{i}-3\hat{j}+6\hat{k})$ is	(IV) $27$

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2025: 30 May Shift 1

Let $\vec{a} = 2\hat{i} - \hat{j}, \vec{b} =- 4\hat{j} + k\,\text{and}\,\vec{c} = \hat{i} + 2\hat{k}$ . If $\vec{d}$ is a vector perpendicular to both $\vec{a}$ and $\vec{b}$ such that $\vec{c} \cdot \vec{d} = 34$ , then $|\vec{d}|$ is equal to

If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c}a,b,c are unit vectors such that a⃗+b⃗+c⃗=0\vec{a} + \vec{b} + \vec{c} = 0a+b+c=0. The value of a⃗.b⃗+b⃗.c⃗+c⃗.a⃗\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}a.b+b.c+c.a is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$ . The value of $\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}$ is