List of top Mathematics Questions on Vector Algebra asked in AIEEE

A unit vector which is perpendicular to the vector $2\hat{i} - \hat{j} + 2\hat{k}$ and is coplanar with the vectors $\hat{i} + \hat{j} - \hat{k}$ and $2\hat{i} + \hat{j} - 2\hat{k}$ is

Let $\vec{a} \,and\, \vec{b}$ be two unit vectors. If the vectors $\vec{c} = \hat{a} + 2\hat{b}$ and $\vec{d} = 5\hat{a} -4\hat{b}$ are perpendicular to each other,then the angle between $\hat{a}$ and $\hat{b}$ is :

Let $\vec{a},\,\vec{b},\,\vec{c}$ be three non-zero vectors which are pairwise non-collinear. If $\vec{a}+3\vec{b}$ is collinear with $\vec{c}$ and $\vec{b}+2\vec{c}$ is collinear with $\vec{a}+3\vec{b}+\vec{c}$ is :

Let $\vec{a} = \hat{j} - \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} - \hat{k}$. Then vector $\vec{b}$ satisfying $\vec{a} \times\vec{b}+\vec{c} = \vec{0}$ and $\vec{a} \cdot\vec{b} = 3$ is

If the vectors $\vec{a} = \hat{i}- \hat{j}+2 \hat{k}, \vec{b} = 2\hat{i}+4 \hat{j}+ \hat{k}$ and $\vec{c} = \lambda\hat{i}+ \hat{j}+\mu \hat{k}$ are mutually orthogonal, then $\left(\lambda, \mu\right) = $

If $\vec{u}, \vec{v}, \vec{w}$ are non-coplanar vectors and $p, q$ are real numbers, then the equality $\left[3\vec{u}\, p\vec{v}\,p\vec{w}\right]-\left[p\vec{v}\,\vec{w}\,q\vec{u}\right]-\left[2\vec{w}\,q\vec{v}\,q\vec{u}\right]=0$ holds for

$A B C$ is a triangle, right angled at $A .$ The resultant of the forces acting along $\overline{A B}, \overline{B C}$ with magnitudes $\frac{1}{A B}$ and $\frac{1}{A C}$ respectively is the force along $\overline{A D},$ where $D$ is the foot of the perpendicular from $A$ onto $B C$. The magnitude of the resultant is

If $C$ is the mid point of $AB$ and $P$ is any point outside $AB$, then :

$A$ and$ B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is contained with them. The resultant of $A$ and $B$ after combining is displaced through a distance :

If $\begin{vmatrix}a&a^{2}&1+a^{3}\\ b&b^{2}&1+b^{3}\\ c&c^{2}&1+c^{3}\end{vmatrix}=0 $ and vectors $(1, a, a^2) (1, b, b^2)$ and $(1, c, c^2)$ are non-coplanar, then the product abc equals