CUET Mathematics 2025 14 May Shift 2 PYQs

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:

Which of the following statements is/are true?

(A) The vector sum of the three sides of a triangle in order is $\vec{0}$

(B) The magnitude $(r)$, direction ratios $(a, b, c)$ and direction cosines $(l, m, n)$ of any vector $\vec{r} = a\hat{i} + b\hat{j} + c\hat{k}$ are related as $l = \frac{a}{r}, m = \frac{b}{r}, n = \frac{c}{r}$

(C) If θ is the angle between two vectors $\vec{a}$ and $\vec{b}$, then their cross product is given as $\vec{a} imes \vec{b} = |\vec{a}||\vec{b}|\sin heta$

(D) The cross product of two vectors is commutative

Choose the correct answer from the options given below:

The projection of the vector $\vec{a} = \vec{i} + 2\vec{j} - 3\vec{k}$ on the vector $2\vec{i} + 6\vec{j} + 3\vec{k}$ is