List of top Mathematics Questions on Vector Algebra asked in CUET (UG)

If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three vectors such that \( \vec{a} + \vec{b} + \vec{c} = 0 \), where \( \vec{a} \) and \( \vec{b} \) are unit vectors and \( |\vec{c}| = 2 \), then the angle between the vectors \( \vec{b} \) and \( \vec{c} \) is:
If \((\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 27\) and \(|\vec{a}| = 2|\vec{b}|\), then \(|\vec{b}|\) is:
\(\text{The distance between the lines } \vec{r} = \hat{i} - 2\hat{j} + 3\hat{k} + \lambda (2\hat{i} + 3\hat{j} + 6\hat{k}) \text{ and } \vec{r} = 3\hat{i} - 2\hat{j} + \hat{k} + \mu (4\hat{i} + 6\hat{j} + 12\hat{k}) \text{ is:}\)
\(\text{The unit vector perpendicular to each of the vectors } \vec{a} + \vec{b} \text{ and } \vec{a} - \vec{b}, \text{ where } \vec{a} = \hat{i} + \hat{j} + \hat{k} \text{ and } \vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}, \text{ is:}\)