List of top Mathematics Questions on Vector Algebra asked in COMEDK UGET

If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( a \neq 0 \) and \( \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}) \), \( |\vec{a}| = |\vec{c}| = 1 \), \( |\vec{b}| = 4 \) and \( |\vec{b} \times \vec{c}| = \sqrt{15} \), if \( \vec{b} - 2\vec{c} = \lambda \vec{a} \) then \( \lambda^2 \) equals:
Find the value of 'b' such that the scalar product of the vector $ \hat{i} + \hat{j} + \hat{k} $ with the unit vector parallel to the sum of the vectors $ 2\hat{i} + 4\hat{j} - 5\hat{k} $ and $ b\hat{i} + 2\hat{j} + 3\hat{k} $ is unity.
If the vectors $ \mathbf{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}, \quad \mathbf{b} = \hat{i} + 2\hat{j} - \hat{k}, \quad \mathbf{c} = m\hat{i} - \hat{j} + 2\hat{k} $ are coplanar, then the value of $ m $ is
If $\vec{a}$ and $\vec{b}$ are two vectors of magnitude $2$, each inclined at an angle $60^\circ$, then angle between $\vec{a}$ and $\vec{a} +\vec{b}$ is
If $|\vec{a} | = 2 , |\vec{b}| = 7$ and $\vec{a} \times \vec{b} = 3 \hat{i} + 2 \hat{j} + 6\hat{k}$ then the angle between $\vec{a}$ and $\vec{b}$ is
If $|\vec{a} | = 15 , |\vec{b} | = 12$ and $|\vec{a} + \vec{b} | = 20 $ then $|\vec{a} - \vec{b} | = $
The volume of the tetrahedron formed by the points $(1, 1, 1 ), (2, 1, 3), (3, 2, 2)$ and $(3, 3, 4)$ in cubic units is
If $\vec{a} = \hat{i} + \lambda \hat{j} + 2 \hat{k}$ and $\vec{b} = \mu \hat{i} + \lambda \hat{j} + 2 \hat{k}$ are orthogonal and if $|\vec{a} | = |\vec{b}|$, then $(\lambda, \mu)$ =
If $\vec{a} , \vec{b} ,\vec{c}$ are unit vectors and $\theta$ is the angle between them, then $| \vec{a} - \vec{b}| = $
The vectors $\vec{a} = x \hat{i} + (x +1) \hat{j} + ( x +2 ) \hat{k} $ $\vec{b} = (x + 3) \hat{i} + (x +4) \hat{j} + ( x + 5 ) \hat{k} $ , and $\vec{c} = (x + 6) \hat{i} + (x + 7 ) \hat{j} + ( x + 8) \hat{k} $ are co-planar for
If $A, B, C, D$ are four points and $\vec{AB} = \vec{DC}$ , then $\vec{AC} + \vec{BD} = $
The value of $[ \vec{a} - \vec{b} \,\,\,\,\,\, \vec{b} - \vec{c} \,\,\,\,\,\, \vec{c} - \vec{a} ]$ where $|\vec{a}| = 1 , |\vec{b} | = 5 , |\vec{c}| = 3 $
The projection of $\vec{a} = 5\hat{i} - \hat{j} + 3 \hat{k}$ on $\vec{b} = 2 \hat{i} + \hat{j} - \hat{k}$ is