CUET Mathematics 2022 4 Aug Shift 1 PYQs

Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}, \vec{b} = -\hat{i} + 2\hat{j} + \hat{k}, \vec{c} = 3\hat{i} + \hat{j}$ be three vectors. If $(\vec{a} + \lambda\vec{b})$ is perpendicular to $\vec{c}$, then the value of $\lambda$ is

Which of the following statements are correct?

(A) If $\vec{a}$ and $\vec{b}$ represent the adjacent sides of a triangle, then its area is $\frac{1}{2}|\vec{a} \times \vec{b}|$

(B) If $\vec{a}$ and $\vec{b}$ represent the adjacent sides of a parallelogram, then its area is $|\vec{a} \times \vec{b}|$

(C) $|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \cos\theta$

(D) If $\vec{a}$ and $\vec{b}$ represent the 'diagonals' of a parallelogram, then its area is $\frac{1}{2}|\vec{a} \times \vec{b}|$

Choose the correct answer from the options given below:

Which of the following cannot be the direction ratios of the straight line $\frac{x-3}{2}=\frac{2-y}{3}=\frac{z+4}{-1}$ ?