Sample QuestionsAlgebra of Vectors questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The position vectors of the points A, B, C are $2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},\ 3\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$ and $\hat{\text{i}}+4\hat{\text{j}}-3\hat{\text{k}}$ respectively. These points,
- Form an isosceles triangle.
- Form a right triangle.
- Are collinear.
- Form a scalene triangle.
View full solution →If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then $\overrightarrow{\text{OA}}+\overrightarrow{\text{OB}}+\overrightarrow{\text{OC}}+\overrightarrow{\text{OD}}=$
- $2\overrightarrow{\text{OG}}$
- $4\overrightarrow{\text{OG}}$
- $5\overrightarrow{\text{OG}}$
- $3\overrightarrow{\text{OG}}$
View full solution →ABCD is a parallelogram with AC and BD as diagonals. Then, $\overrightarrow{\text{AC}}-\overrightarrow{\text{BD}}=$
- $4\overrightarrow{\text{AB}}$
- $3\overrightarrow{\text{AB}}$
- $2\overrightarrow{\text{AB}}$
- $\overrightarrow{\text{AB}}$
View full solution →If $\vec{\text{a}}\text{ and }\vec{\text{b}}$ are two collinear vectors, then which of the follwoing are incorrect?
- $\vec{\text{b}}=\lambda\vec{\text{a}}$ for some scalar $\lambda$
- $\vec{\text{a}}=\pm\vec{\text{b}}$
- The respective components of $\vec{\text{a}}\text{ and }\vec{\text{b}}$ are proportional.
- Both the vectors $\vec{\text{a}}\text{ and }\vec{\text{b}}$ have the same direction but different magnitudes.
View full solution →Let G be the centroid of $\triangle{\text{ABC}}$. if $\overrightarrow{\text{AB}}=\vec{\text{a}},\overrightarrow{\text{AC}}=\vec{\text{b}}$, then the bisector $\overrightarrow{\text{AG}}$, in terms of $\vec{\text{a}}$ and $\vec{\text{b}}$ is,
- $\frac{2}3\big(\vec{\text{a}}+\vec{\text{b}}\big)$
- $\frac{1}6\big(\vec{\text{a}}+\vec{\text{b}}\big)$
- $\frac{1}3\big(\vec{\text{a}}+\vec{\text{b}}\big)$
- $\frac{1}2\big(\vec{\text{a}}+\vec{\text{b}}\big)$
View full solution →Define position vector of a point.
If $\vec{\text{a}}$ ia a non-zero vector of modulus a and m is a non-zero scalar such that $\text{m}\vec{\text{a}}$ is the unit vector, write the value of m.
View full solution →Write $\overrightarrow{\text{PQ}}+\overrightarrow{\text{RP}}+\overrightarrow{\text{QR}}$ in the simplified form.
View full solution →If $\vec{\text{a}}\text{ and }\vec{\text{b}}$ are two non-collinear vectors such that $\text{x}\vec{\text{a}}+\text{y}\vec{\text{b}}=\vec0$, Then write the values of x and y.
View full solution →A vector $\vec{\text{r}}$ is inclined at equal acute angles to x-axis, y-axis and z-axis. If $|\vec{\text{r}}|=6$ units, find $\vec{\text{r}}$.
View full solution →Write a vector in the direction of vector $5\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$ which has magnitude of 8 unit.
View full solution →If G denots the centroid of $\triangle\text{ABC}$, then write the value of $\overrightarrow{\text{GA}}+\overrightarrow{\text{GB}}+\overrightarrow{\text{GC}}$.
View full solution →If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are position vectors of the points A, B and C respectively, write the value of$\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}+\overrightarrow{\text{AC}}$.
View full solution →What is the cosine of the angle with the vector $\sqrt2\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ makes with y-axis?
View full solution →ABCD is a parallelogram. If the coordinates of A, B, C are (-2, -1), (3, 0) and (1, -2) respectively, find the coordinates of D.
If D, E, F are the mid-points of side BC, CA and AB respectively of a triangle ABC, write the value of $\overrightarrow{\text{AD}}+\overrightarrow{\text{BE}}+\overrightarrow{\text{CF}}$.
View full solution →A vector $\vec{\text{r}}$ is inclined at equal angles to the three axes. If the magnitude of $\vec{\text{r}}$ is $2\sqrt3$, find $\vec{\text{r}}$.
View full solution →If the position vector $\vec{\text{a}}$ of a point (12, n) is such that $\big|\vec{\text{a}}\big|=13$, find the value (s) of n.
View full solution →A vector $\vec{\text{r}}$ is inclined to x-axis at 45º and y-axis at 60º. If $|\vec{\text{r}}|=8$ units, find $\vec{\text{r}}$.
View full solution →If $\vec{\text{a}}\text{ and }\vec{\text{b}}$ are two non-collinear vectors having the same initial point. What are the vectors represented by $\vec{\text{a}}+\vec{\text{b}}\text{ and }\vec{\text{a}}-\vec{\text{b}}$.
View full solution →The two vectors $\hat{\text{j}}+\hat{\text{k}}$ and $3\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}}$ represents the sides $\overrightarrow{\text{AB}}$ and $\overrightarrow{\text{AC}}$ respectively of a triangle ABC. Find the length of the median through A.
View full solution →If P is a point and ABCD is a quadrilateral and $\overrightarrow{\text{AP}}+\overrightarrow{\text{PB}}+\overrightarrow{\text{PD}}=\overrightarrow{\text{PC}}$, show that ABCD is a parallelogram.
View full solution →Prove that the points $\hat{\text{i}}-\hat{\text{j}},\ 4\hat{\text{i}}+3\hat{\text{j}}+\hat{\text{k}}$ and $2\hat{\text{i}}-4\hat{\text{j}}+5\hat{\text{k}}$ are the vertices of a right-angled triangle.
View full solution →Show that the points $\text{A}\big(2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}\big),\ \text{B}\big(\hat{\text{i}}-3\hat{\text{j}}-5\hat{\text{k}}\big),$ $\text{C}\big(3\hat{\text{i}}-4\hat{\text{j}}-4\hat{\text{k}}\big)$ are the vertices of a right angled triangle.
View full solution →Two collinear vectors are always equal in magnitude.
Two collinear vectors having the same magnitude are equal.
Two vectors having same magnitude are collinear.
Answer the following as true or false:
$\vec{\text{a}}\text{ and }\vec{\text{a}}$ are collinear.
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