CUET Mathematics 2025 3 June Shift 2 PYQs

The unit vector perpendicular to each of the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$, where $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}+2 \hat{j}+3 \hat{k}$, 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:

If A (3, 2), B (1, -1) and C (2, 1) are three vertices of a parallelograms ABCD, then its area (in sq.units) is equal to