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 in a $\triangle\text{ABC}$, $\text{A}=(0,0),\ \text{B}=(3,3\sqrt3),\ \text{C}=(-3\sqrt3,3)$, then the vecctor of magnitude $2\sqrt2$ units directed along AO, where O is the circumcenter of $\triangle\text{ABC}$ is,
- $(1-\sqrt3)\hat{\text{i}}+(1+\sqrt3)\hat{\text{j}}$
- $(1+\sqrt3)\hat{\text{i}}+(1-\sqrt3)\hat{\text{j}}$
- $(1+\sqrt3)\hat{\text{i}}+(\sqrt3-1)\hat{\text{j}}$
- None of these
View full solution →If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ and $\vec{\text{d}}$ are the position vector of points A, B, C, D such that no three of them are collinear and $\vec{\text{a}}+\vec{\text{c}}=\vec{\text{b}}+\vec{\text{d}}$, then ABCD is a,
- Rhombus.
- Rectangle.
- Square.
- Parallelogram.
View full solution →If OACB is a parallelogram with $\overrightarrow{\text{OC}}=\vec{\text{a}}$ and $\overrightarrow{\text{AB}}=\vec{\text{b}}$, then $\overrightarrow{\text{OA}}=$
- $\big(\vec{\text{a}}+\vec{\text{b}}\big)$
- $\big(\vec{\text{a}}-\vec{\text{b}}\big)$
- $\frac{1}2\big(\vec{\text{b}}-\vec{\text{a}}\big)$
- $\frac{1}2\big(\vec{\text{a}}-\vec{\text{b}}\big)$
View full solution →In figure, which of the following is not true? - $\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}+\overrightarrow{\text{CA}}=\vec0$
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$\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}-\overrightarrow{\text{AC}}=\vec0$
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$\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}-\overrightarrow{\text{CA}}=\vec0$
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$\overrightarrow{\text{AB}}-\overrightarrow{\text{CB}}+\overrightarrow{\text{CA}}=\vec0$
View full solution →Classify the following measures as scalar and vector:
45º
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 →View full solution →If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ represent the sides of a triangle taken in order, then write the value of $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$.
View full solution →If a vector makes angles $\alpha,\beta,\gamma$ with OX, OY and OZ respectively. then write the value of $\sin^2\alpha+\sin^2\beta+\sin^2\gamma$.
View full solution →If P, Q and R are three collinear points such that $\overrightarrow{\text{PQ}}=\vec{\text{a}}\text{ and }\overrightarrow{\text{QR}}=\vec{\text{b}}$. Find the vector $\overrightarrow{\text{PR}}$.
View full solution →Write a vector of magnitude 12 units which makes 45º angle with x-axis, 60º angle with y-axis and an obtuse angle with z-axis.
A unit vector $\vec{\text{r}}$ makes angles $\frac{\pi}3\text{ and }\frac{\pi}2$ with $\hat{\text{j}}\text{ and } \hat{\text{k}}$ respectively and an acute angle $\theta$ with $\hat{\text{i}}$. Find $\theta$.
View full solution →ABCD is a parallelogram and P is the point of intersection of its diagonals. If O is the origin of reference, show that $\overrightarrow{\text{OA}}+\overrightarrow{\text{OB}}+\overrightarrow{\text{OC}}+\overrightarrow{\text{OD}}=4\ \overrightarrow{\text{OP}}$.
View full solution →Find a vector $\vec{\text{r}}$ of magnitude $3\sqrt{2}$ units which makes an angle of $\frac{\pi}{4}$ and $\frac{\pi}{2}$ with and z-axes respectively.
View full solution →Find the position vector of the mid-point of the vector joining the points $\text{P}\big(2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}\big)$ and $\text{Q}\big(4\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}\big)$.
View full solution →Find a vector of magnitude of 5 units parallel to the resultant of the vectors $\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$.
View full solution →Using vectors, find the value of $\lambda$ such that the points ($\lambda$, -10, 3), (1, -1, 3) and (3, 5, 3) are collinear.
View full solution →In Figure ABCD is a regular hexagon, which vectors are:
- Collinear.
- Equal.
- Co-initial.
- Collinear but not equal.
Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.
If O is a point in space, ABC is a triangle and D, E, F are the mid-points of the sides BC, CA and AB respectively of the triangle, prove that $\overrightarrow{\text{OA}}+\overrightarrow{\text{OB}}+\overrightarrow{\text{OC}}=\overrightarrow{\text{OD}}+\overrightarrow{\text{OE}}+\overrightarrow{\text{OF}}$.
View full solution →Five forces $\overrightarrow{\text{AB}},\ \overrightarrow{\text{AC}},\ \overrightarrow{\text{AD}},\ \overrightarrow{\text{AE}}\text{ and }\overrightarrow{\text{AF}}$ act at the vertex of a regular hexagon ABCDEF. Prove that the resultant is: $6\ \overrightarrow{\text{AO}}$, where o is the center of hexagon.
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 →