MHT CET
Mathematics
Vector Algebra
Previous Years Questions

If $$\bar{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \bar{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}, \bar{c}=2 \hat{i}-\hat{j}+4 \hat{k}$$, then a vector $$\overline{\mat... The unit vector perpendicular to each of the vectors$$\bar{a}+\bar{b}$$and$$\bar{a}-\bar{b}$$, where$$\bar{a}=\hat{i}+\hat{j}+\hat{k}$$and$$\ove...
Let $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \bar{b}=\hat{i}+\hat{j}$$ and $$\bar{c}$$ be a vector such that $$|\bar{c}-\bar{a}|=4,|(\bar{a} \times \bar... If the area of the parallelogram with$$\bar{a}$$and$$\bar{b}$$as two adjacent sides is$$16 \mathrm{sq}$$. units, then the area of the parallelogr... If$$\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\m...
If $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mat... If the volume of the parallelopiped is$$158 \mathrm{~cu}$$. units whose coterminus edges are given by the vectors$$\bar{a}=(\hat{i}+\hat{j}+n \hat{k...
If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors such that $$\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}}+\overline{\mathrm{c}})+\overline{\mat... Let$$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}$$and$$\bar{b}=\hat{i}+\hat{j}$$. If$$\bar{c}$$is a vector such that$$\overline{\mathrm{a}} \cdot \overl...
If $$\quad \overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \quad \overline{\mathrm{b}}=2 \hat{\mathrm{j}}-\hat{\mathrm{k}} \quad$$ and $$\qua... Let$$\bar{a}, \bar{b}$$and$$\bar{c}$$be three unit vectors such that$$\bar{a} \times(\bar{b} \times \bar{c})=\frac{\sqrt{3}}{2}(\bar{b}+\bar{c})... If $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are two unit vectors such that $$\overline{\mathrm{a}}+2 \overline{\mathrm{b}}$$ and $$5 \b... If$$(\bar{a} \times \bar{b}) \times \bar{c}=-5 \bar{a}+4 \bar{b}$$and$$\bar{a} \cdot \bar{b}=3$$, then the value of$$\bar{a} \times(\bar{b} \times... If $$\bar{p}=\hat{i}+\hat{j}+\hat{k}$$ and $$\bar{q}=\hat{i}-2 \hat{j}+\hat{k}$$. Then a vector of magnitude $$5 \sqrt{3}$$ units perpendicular to the... If $$\bar{a}$$ and $$\bar{b}$$ are two unit vectors such that $$\bar{a}+2 \bar{b}$$ and $$5 \bar{a}-4 \bar{b}$$ are perpendicular to each other, then ... If $$\overline{\mathrm{a}}=\mathrm{m} \overline{\mathrm{b}}+\mathrm{nc}$$, where $$\overline{\mathrm{a}}=4 \hat{\mathrm{i}}+13 \hat{\mathrm{j}}-18 \ha... If the volume of tetrahedron, whose vertices are with position vectors$$\hat{i}-6 \hat{j}+10 \hat{k},-\hat{i}-3 \hat{j}+7 \hat{k}, 5 \hat{i}-\hat{j}+... Scalar projection of the line segment joining the points $$\mathrm{A}(-2,0,3), \mathrm{B}(1,4,2)$$ on the line whose direction ratios are $$6,-2,3$$ i... If $$\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\m... The vector projection of$$\overline{\mathrm{AB}}$$on$$\overline{\mathrm{CD}}$$, where$$A \equiv(2,-3,0), B \equiv(1,-4,-2), C \equiv(4,6,8)$$and ... The vectors are$$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \bar{b}=\hat{i}+\hat{j}$$. If$$\bar{c}$$is a vector such that$$\bar{a} \cdot \bar{c}=|\bar{c... If $$\bar{a}=\hat{i}+2 \hat{j}+\hat{k}, \bar{b}=\hat{i}-\hat{j}+\hat{k}, \bar{c}=\hat{i}+\hat{j}-\hat{k}$$, then a vector in the plane of $$\bar{a}$$ ... Let $$\bar{a}, \bar{b}, \bar{c}$$ be three non-zero vectors, such that no two of them are collinear and $$(\bar{a} \times \bar{b}) \times \bar{c}=\fra...$$\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$$, then vector$$\... The magnitude of the projection of the vector $$2 \hat{i}+\hat{j}+\hat{k}$$ on the vector perpendicular to the plane containing the vectors $$\hat{i}+... If$$\bar{a}, \bar{b}$$and$$\bar{c}$$are any three non-zero vectors, then$$(\bar{a}+2 \bar{b}+\bar{c}) \cdot[(\bar{a}-\bar{b}) \times(\bar{a}-\bar... Vectors $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are such that $$|\overline{\mathrm{a}}|=1 ;|\overline{\mathrm{b}}|=4$$ and $$\bar{a} \... Two adjacent sides of a parallelogram are$$2 \hat{i}-4 \hat{j}+5 \hat{k}$$and$$\hat{i}-2 \hat{j}-3 \hat{k}$$, then the unit vector parallel to its ... If$$\mathrm{D}, \mathrm{E}$$and$$\mathrm{F}$$are the mid-points of the sides$$\mathrm{BC}$$,$$\mathrm{CA}$$and$$\mathrm{AB}$$of triangle$$\m... If two vertices of a triangle are $$\mathrm{A}(3,1,4)$$ and $$\mathrm{B}(-4,5,-3)$$ and the centroid of the triangle is $$G(-1,2,1)$$, then the third ... Let two non-collinear vectors $$\hat{a}$$ and $$\hat{b}$$ form an acute angle. A point $$\mathrm{P}$$ moves, so that at any time $$t$$ the position ve... The distance of the point having position vector $$\hat{i}-2 \hat{j}-6 \hat{k}$$, from the straight line passing through the point $$(2,-3,-4)$$ and p... The scalar product of the vector $$\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$$ with a unit vector along the sum of the vectors $$2 \hat{i}+4 ... If$$[(\bar{a}+2 \bar{b}+3 \bar{c}) \times(\bar{b}+2 \bar{c}+3 \bar{a})] \cdot(\bar{c}+2 \bar{a}+3 \bar{b})=54$$then the value of$$\left[\begin{arra... The volume of parallelopiped, whose coterminous edges are given by $$\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}},... If$$\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\m... If $${\pi \over 2} ... If$$|\bar{a} \times \bar{b}|^2+(\bar{a} \cdot \bar{b})^2=144$$and$$|\bar{a}|=4$$, then$$|\bar{b}|=$$The distance between parallel lines$$\begin{aligned} & \bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-2 \hat{k}) \text { and } \\ & \b... The vertices of triangle $$\mathrm{ABC}$$ are $$\mathrm{A} \equiv(3,0,0) ; \mathrm{B} \equiv(0,0,4) ; \mathrm{C} \equiv(0,5,4)$$. Find the position ve... In a quadrilateral PQRS, M and N are mid-points of the sides PQ and RS respectively. If $$\overline {PS} + \overline {QR} = t\overline {MN}$$, then... If vectors $$\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$$ and $$\bar{c}=3 \hat{i}+\hat{j}+2 \hat{k}$$ are such that, $$... If$$\bar{a}=3 \hat{i}-5 \hat{j}, \bar{b}=6 \hat{i}+3 \hat{j}$$are two vectors and$$\bar{c}$$is a vector such that$$\bar{c}=\bar{a} \times \bar{b}... If $$|\bar{a}|=3,|\bar{b}|=4,|\bar{a}-\bar{b}|=5$$, then $$|\bar{a}+\bar{b}|=$$ $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are vectors such that $$|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=4,|\... If$$[\bar{a} \bar{b} \bar{c}]=4$$, then the volume (in cubic units) of the parallelopiped with$$\bar{a}+2 \bar{b}, \bar{b}+2 \bar{c}$$and$$\overli... $$\overline{\mathrm{a}}, \overline{\mathrm{b}}$$ and $$\overline{\mathrm{c}}$$ are three vectors such that $$\overline{\mathrm{a}}+\overline{\mathrm{b... If area of the parallelogram with$$\bar{a}$$and$$\bar{b}$$as two adjacent sides is 20 square units, then the area of the parallelogram having$$3 ... If $$\bar{r}=-4 \hat{i}-6 \hat{j}-2 \hat{k}$$ is a linear combination of the vectors $$\bar{a}=-\hat{i}+4 \hat{j}+3 \hat{k}$$ and $$\bar{b}=-8 \hat{i}... If the volume of a tetrahedron whose conterminous edges are$$\vec{\mathrm{a}}+\vec{\mathrm{b}}, \vec{\mathrm{b}}+\vec{\mathrm{c}}, \vec{\mathrm{c}}+\... If $$\overline{\mathrm{e}}_1, \overline{\mathrm{e}}_2$$ and $$\overline{\mathrm{e}}_1+\overline{\mathrm{e}}_2$$ are unit vectors, then the angle betwe... If $$\overline{\mathrm{a}}, \overline{\mathrm{b}} , \overline{\mathrm{c}}$$ are three vectors which are perpendicular to $$\overline{\mathrm{b}}+\over...$$(2 \hat{\mathrm{i}}+6 \hat{\mathrm{i}}+27 \hat{\mathrm{k}}) \times(\hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\mu \hat{\mathrm{k}})=\overline{0}\$, t...
EXAM MAP
Joint Entrance Examination