CUET Mathematics 2022 4 Aug Shift 1 PYQs

Given that $\vec{a} = -3\hat{i} - 6\hat{j} + 4\hat{k}$, $\vec{b} = 9\hat{i} - λ\hat{j} - 12\hat{k}$. If $\vec{a} \times \vec{b} = \vec{0}$, then the value of λ is

If $\theta$ is an acute angle and the vector $\vec{a} = (\sin \theta)\vec{i} + (\cos\theta)\vec{j}$ is perpendicular to the vector $\vec{b} = i - \sqrt{3}j$ then $\theta$ is equal to

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 $\vec{a} \times \vec{b} = |\vec{a}||\vec{b}|\sin \theta$

(D) The cross product of two vectors is commutative

Choose the correct answer from the options given below: