List of top Mathematics Questions on Vector Algebra asked in MET

In a trapezoid of the vector \( \vec{BC} = \lambda \vec{AD} \). We will, then find that \( \vec{P} = \vec{AC} + \vec{BD} \) is collinear with \( \vec{AD} \). If \( \vec{P} = \mu \vec{AD} \), then

If \( P(\vec{p}) \), \( Q(\vec{q}) \), \( R(\vec{r}) \), and \( S(\vec{s}) \) are four points such that \( 3\vec{p} + 8\vec{q} = 6\vec{r} + 5\vec{s} \), then the lines PQ and RS are

Let \( \vec{a} = 2\hat{i} + \hat{j} - 2\hat{k} \) and \( \vec{b} = \hat{i} + \hat{j} \), if \( \vec{c} \) is a vector such that \( \vec{a} \cdot \vec{c} = |\vec{c}| \), \( |\vec{c} - \vec{a}| = 2\sqrt{2} \), and the angle between \( \vec{a} \times \vec{b} \) and \( \vec{c} \) is \( 30^\circ \), then \( |(\vec{a} \times \vec{b}) \times \vec{c}| \) is equal to

Consider a tetrahedron with faces \( F_1, F_2, F_3, F_4 \). Let \( \vec{v_1}, \vec{v_2}, \vec{v_3}, \vec{v_4} \) be area vectors perpendicular to these faces in the outward direction, then \( |\vec{v_1} + \vec{v_2} + \vec{v_3} + \vec{v_4}| \) equals

If \( V \) is the volume of the parallelepiped with edges \( \vec{a}, \vec{b}, \vec{c} \), then the volume of the parallelepiped with edges \( \vec{\alpha}, \vec{\beta}, \vec{\gamma} \) (defined by dot products) is

Define the length of \( a\hat{i} + b\hat{j} + c\hat{k} \) as \( |a| + |b| + |c| \). This definition coincides with the usual definition if and only if

If \( \vec{u} = \hat{i} + \hat{j}, \vec{v} = \hat{i} - \hat{j}, \vec{w} = \hat{i} + 2\hat{j} + 3\hat{k} \) and \( \hat{n} \) is a unit vector such that \( \vec{u} \cdot \hat{n} = 0 \) and \( \vec{v} \cdot \hat{n} = 0 \), then \( |\vec{w} \cdot \hat{n}| \) is