List of top Mathematics Questions on Scalar and Vector Product asked in CUET (UG)

If the direction vectors of two straight lines are given by \( \vec{m} = \hat{i} + \hat{j} + 0\hat{k} \) and \( \vec{n} = \hat{i} + 0\hat{j} + \hat{k} \), calculate the value of \( \cos\phi \) representing the acute angle between them.

The total area of a parallelogram constructed with adjacent vector sides given by \( \vec{a} = \hat{i} - \hat{j} + 3\hat{k} \) and \( \vec{b} = 2\hat{i} - 7\hat{j} + \hat{k} \) is equal to:

A unit vector perpendicular to the vectors \[ \hat i-\hat j \] and \[ \hat i+\hat j \] is: