List of top Mathematics Questions on Vector Algebra asked in TS EAMCET

In a triangle ABC, if $\vec{BC}=\hat{i}-2\hat{j}+2\hat{k}$ and $\vec{CA}=6\hat{i}+3\hat{j}-2\hat{k}$, then the perimeter of the triangle is

In a quadrilateral ABCD, $\angle A = \frac{2\pi}{3}$ and AC is the bisector of angle A. If $15|AC| = 5|AD| = 3|AB|$, then the angle between $\vec{AB}$ and $\vec{BC}$ is

$\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar and mutually perpendicular vectors of same magnitude K. $\vec{r}$ is any vector satisfying $\vec{a}\times((\vec{r}-\vec{b})\times\vec{a}) + \vec{b}\times((\vec{r}-\vec{c})\times\vec{b}) + \vec{c}\times((\vec{r}-\vec{a})\times\vec{c}) = \vec{0}$, then $\vec{r} =$

Two adjacent sides of a triangle are represented by the vectors $2\vec{i}+\vec{j}-2\vec{k}$ and $2\sqrt{3}\vec{i}-2\sqrt{3}\vec{j}+\sqrt{3}\vec{k}$. Then the least angle of the triangle and perimeter of the triangle are respectively

A plane $\pi_1$ contains the vectors $\vec{i}+\vec{j}$ and $\vec{i}+2\vec{j}$. Another plane $\pi_2$ contains the vectors $2\vec{i}-\vec{j}$ and $3\vec{i}+2\vec{k}$. $\vec{a}$ is a vector parallel to the line of intersection of $\pi_1$ and $\pi_2$. If the angle $\theta$ between $\vec{a}$ and $\vec{i}-2\vec{j}+2\vec{k}$ is acute, then $\theta=$

Let $\vec{a} = \hat{i} +2\hat{j}+3\hat{k}$, $\vec{b}=2\hat{i}-3\hat{j}+\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}-2\hat{k}$ be three vectors. If $\vec{r}$ is a vector such that $\vec{r}\cdot\vec{a} = 0$, $\vec{r}\cdot\vec{b} = -2$ and $\vec{r}\cdot\vec{c} = 6$ then $\vec{r}\cdot(3\hat{i}+\hat{j}+\hat{k})= $

If $\hat{i}+\hat{j}+\hat{k}$, $a_1\hat{i}+b_1\hat{j}+c_1\hat{k}$, $a_2\hat{i}+b_2\hat{j}+c_2\hat{k}$, $a_3\hat{i}+b_3\hat{j}+c_3\hat{k}$ are the position vectors of the points A, B, C, D respectively, $\frac{2}{3}(\hat{i}+\hat{j}+\hat{k})$ is the position vector of the centroid of the triangular face BCD of the tetrahedron ABCD, and if $\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}$ is the position vector of the centroid of the tetrahedron, then $2\alpha+\beta+\gamma =$

If $\vec{a}=\hat{i}-2\hat{j}+2\hat{k}$ and $\vec{b}=9\hat{i}+6\hat{j}-18\hat{k}$ are two vectors, then $\frac{\text{Projection of } \vec{b} \text{ on } \vec{a}}{\text{Projection of } \vec{a} \text{ on } \vec{b}} =$

Let $\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + p\hat{k}$ be two vectors. If $(\vec{a}, \vec{b}) = 60^\circ$, then $p =$

If $\vec{a} = \hat{i} + \sqrt{11}\hat{j} - 2\hat{k}$ and $\vec{b} = \hat{i} + \sqrt{11}\hat{j} - 10\hat{k}$ are two vectors then the component of $\vec{b}$ perpendicular to $\vec{a}$ is

$7\hat{i}-4\hat{j}+7\hat{k}, \hat{i}-6\hat{j}+10\hat{k}, -\hat{i}-3\hat{j}+4\hat{k}, 5\hat{i}-\hat{j}+\hat{k}$ are the position vectors of the points A, B, C, D respectively. If $p\hat{i} + q\hat{j} + r\hat{k}$ is the position vector of the point of intersection of the diagonals of the quadrilateral ABCD, then $p+q+r=$

If $\vec{a} = (x+2y-3)\hat{i} + (2x-y+3)\hat{j}$ and $\vec{b} = (3x-2y)\hat{i} + (x-y+1)\hat{j}$ are two vectors such that $\vec{a} = 2\vec{b}$, then $y-5x=$