CUET Mathematics - If a, b, c are vectors such that a + b + c = 0 and |a| = 1, |b| = 2, |c| = 5, then the expression a*b + b*c + c*a equals | PYQs + Solutions

30 May Shift 1

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

15 May Shift 1

If $\vec{p}$ and $\vec{q}$ are two unit vectors such that $|\vec{p} + \vec{q}| = \sqrt{2}$ , then which of the following are correct?

(A) $|\vec{p}| = |\vec{q}| = 1$

(B) $\vec{p}$ and $\vec{q}$ are orthogonal vectors

(C) $\vec{p}$ and $\vec{q}$ are collinear vectors

(D) $(4\vec{p} - \vec{q}).(2\vec{p} + \vec{q}) = 7$

Choose the correct answer from the options given below:

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) $\vec{a} imes \vec{b}$ 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) $\frac{1}{\sqrt{33}}(4\hat{i} + \hat{j} + 4\hat{k})$

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CUET Mathematics 2025 21 May Shift 1 PYQs

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