List of top Mathematics Questions on Product of Two Vectors asked in COMEDK UGET

For any vector \( \vec{p} \), the value of \( 2\left[|\vec{p}\times \hat{i}|^2 + |\vec{p}\times \hat{j}|^2 + |\vec{p}\times \hat{k}|^2\right] \) is

If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( \vec{a}\cdot\vec{b} = |\vec{a}\times\vec{b}| \) then the angle between \( \vec{a} \) and \( \vec{b} \) is

If \( |\mathbf{a}| = 2\sqrt{2} \) and \( |\mathbf{b}| = 3 \) and the angle between \( \mathbf{a} \) and \( \mathbf{b} \) is \( \frac{\pi}{4} \), and if a parallelogram is constructed with adjacent sides \( \mathbf{p} = 2\mathbf{a} - 3\mathbf{b} \) and \( \mathbf{q} = \mathbf{a} + \mathbf{b} \), then the product of the lengths of both diagonals is: