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

Find the angle between the vectors \[ \vec{a}=\hat{i}+\hat{j}-\hat{k} \] and \[ \vec{b}=\hat{i}-\hat{j}+\hat{k}. \]
If two vectors \( \vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k} \) and \( \vec{b} = 4\hat{i} - 2\hat{j} - 2\hat{k} \) are perpendicular to each other, determine the value of the scalar constant \( \lambda \).
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: