List of top Mathematics Questions on Properties of Vectors asked in CUET (UG)

If \(\vec{a}\) and \(\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) for \( \sqrt{3}\vec{a} - \vec{b} \) to be a unit vector is given by :
If vectors $ \mathbf{u}, \mathbf{v}, $ and $ \mathbf{w} $ satisfy $ \mathbf{u} + \mathbf{v} + \mathbf{w} = 0 $, and $ \mathbf{u} $ and $ \mathbf{v} $ are unit vectors, while $ |\mathbf{w}| = \sqrt{3} $, then the angle between $ \mathbf{v} $ and $ \mathbf{w} $ is:
Direction cosines of a vector perpendicular to $ \mathbf{a} = \hat{i} + 2\hat{j} + 3\hat{k} $ and $ \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} $ are:
The angle between vectors $ \mathbf{a} = \hat{i} + \hat{j} - 2\hat{k} $ and $ \mathbf{b} = 3\hat{i} - \hat{j} + 2\hat{k} $ is: