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Recent questions in Vector Algebra
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CBSE XII
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Math
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Vector Algebra
Using vector method, prove that if the diagonals of a parallelogram are equal in length, then it is a rectangle.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q21
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Prove that the perpendicular bisectors of a triangle are concurrent.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q20
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Prove that the altitudes of a triangle are concurrent.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q19
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method, find the angle between two diagonals of a cube?
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q18
p36
medium
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method prove that : $a)\;\sin (A+B)=\sin A\cos B+\cos A\sin B$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q17
q17-a
p36
medium
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
In a triangle ABC, prove that $\Large\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q16
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
If $\Large\frac{1}{a},\frac{1}{b},\frac{1}{c}$are the $\large p^{th},q^{th}and\;r^{th}\;$ terms of an AP and $ \bar{u}=(q-r)\bar{i}+(r-p)\bar{j}+(p-q)\bar{k}\;and\;\bar{v}=\large\frac{1}{a}\bar{i}+\frac{1}{b}\bar{j}+\frac{1}{c}\bar{k}$ then prove that $\bar{u}\; and\;\bar{v}$ are orthogonal vectors.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q15
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Prove that the area of a paralellogram with diagonals $\bar{a}\;and\;\bar{b}\;is\;\frac{1}{2}|\bar{a} \times \bar{b}|$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q14
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Let $ \bar{a},\bar{b},\;and\;\bar{c}$ be three vectors such that $|\bar{a}|=3,|\bar{b}|=4,|\bar{c}|=5$ and each one of them being perpendicular to sum of the other two, find $ |\bar{a}+\bar{b}+\bar{c}|$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q13
p35
medium
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
L and M are the mid-points of sides BC & DC of a paralellogram ABCD. Prove that $ \overline{AL}+\overline{AM}=\frac{3}{2}\overline{AC}$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q12
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Vectors $ 2\bar{i}-\bar{j}+2\bar{k}\;and\;\bar{i}+\bar{j}-3\bar{k}$ act along two adjacent sides of a parallelogram. Find the angle between the diagonals of the parallelogram.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q11
p35
easy
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
What is the area of the parallelogram having diagonals $ 3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$?
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q10
p35
easy
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Show that in a triangle ABC the perpendicular of the point $ C $ from the line joining $ the\:points\:A\:and\:B\:is\;\Large\frac{|\bar{a} \times \bar{b}+\bar{b} \times \bar{c}+\bar{c} \times \bar{a}|}{|\bar{b}-\bar{a}|}$(Hint : use area of triangle =$\frac{1}{2}$bh)
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q9
p35
math
asked
Feb 4, 2013
by
meena.p
0
answers
If $ \hat{a}\;and\;\hat{b}$ are unit vectors inclined at an angle $\theta$,then prove that\[(a)\;\cos \frac{\theta}{2}=\frac{1}{2}|\hat{a}+\hat{b}|\qquad(b)\;\tan \frac{\theta}{2}=\frac {|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q8
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Prove that angle in a semi-circle is a right angle.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q7
p35
medium
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
If $ \bar{a}\;and\;\bar{b}$ are vectors,prove that $ |\bar{a} \times \bar{b}|^2+(\bar{a}.\bar{b})^2=|\bar{a}|^2.|\bar{b}|^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q6
p35
easy
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Prove Cauchy - Schawarz inequality : $(\bar{a}.\bar{b})^2\leq|\bar{a}|^2.|\bar{b}|^2$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q5
p35
math
asked
Feb 4, 2013
by
meena.p
0
answers
Prove the triangle inequality $\bigg|\overrightarrow{a}+\overrightarrow{b}\bigg|\leq\bigg|\overrightarrow{a}\bigg|+\bigg|\overrightarrow{b}\bigg|$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q4
p35
medium
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
If $ \overrightarrow {a}+ \overrightarrow {b}+ \overrightarrow {c}=\overrightarrow 0$ show that $ \overrightarrow {a} \times \overrightarrow {b}=\overrightarrow {b} \times \overrightarrow {c}=\overrightarrow {c} \times \overrightarrow {a}$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q3
p35
medium
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
If $\bar{\alpha}=3\bar{i}-\bar{j}\;and\;\bar{\beta}=2\bar{i}+\bar{j}-\bar{k}.$ Express $ \bar{\beta}$ as a sum of two vectors $ \bar{\beta_1}\;and\;\bar{\beta_2},\;where \; \bar{\beta_1}$ is parallel to $ \bar{\alpha}\;and\; \bar{\beta_2}$ is prependicular to $ \bar{\alpha}$
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q2
p35
difficult
sec-b
math
asked
Feb 4, 2013
by
meena.p
1
answer
Find the unit vector perpendicular to both the vectors\[\bar{a}=4\bar{i}-\bar{j}-3\bar{k}\;and\;\bar{b}=2\bar{i}+2\bar{j}-\bar{k}\]
cbse
class12
additionalproblem
kvquestionbank2012
ch10
p35
math
asked
Feb 4, 2013
by
meena.p
0
answers
True-or-false: If $\overrightarrow{a}$ and $\overrightarrow{b}$ are adjacent sides of a rhombus,then $\overrightarrow{a}.\overrightarrow{b}=0$
cbse
class12
ch10
q45
p219
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
True-or-False: The formula $(\overrightarrow{a}+\overrightarrow{b})^2=\mid{\overrightarrow{a}\mid}^2+\mid{\overrightarrow{b}\mid}^2\;+2\mid\overrightarrow{a}\mid.\mid\overrightarrow{b}\mid$ is valid for non-zero vectors $\overrightarrow{a}$ and $\overrightarrow{b}.$
cbse
class12
ch10
q44
p219
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
True-or-False: If $\mid \overrightarrow{a}+\overrightarrow{b}\mid=\mid \overrightarrow{a}-\overrightarrow{b}\mid$,then the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are orthogonal.
cbse
class12
ch10
q43
p219
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
True-or-False: Position vector of a point P is a vector whose initial point is origin.
cbse
class12
ch10
q42
p219
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
True-or-False: If $\mid\overrightarrow{ a}\mid=\mid\overrightarrow {b}\mid$,then necessarily it implies $\overrightarrow{ a}=\overrightarrow {b}.$
cbse
class12
ch10
q41
p219
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow a$ is any non-zero vector ,then $(\overrightarrow a.\hat i)\hat i\;+(\overrightarrow a.\hat j)\hat j\;+(\overrightarrow a.\hat k)\hat k$ equals__________.
cbse
class12
ch10
q40
p219
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If ${\mid\overrightarrow{a}\times\overrightarrow{b}\mid}^2$=${\mid\overrightarrow{a}.\overrightarrow{b}\mid}^2=144$ and$\mid\overrightarrow{a}\mid=4,$ then $\mid\overrightarrow{b}\mid$ is equal to ________.
cbse
class12
ch10
q39
p219
exemplar
medium
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The value of the expression ${\mid \overrightarrow{a}\times \overrightarrow{b}\mid}^2+(\overrightarrow{a}.\overrightarrow{b})^2$ is _________.
cbse
class12
ch10
q38
p219
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The values of k for which $\mid k\overrightarrow{a}\mid\le\mid\overrightarrow{a}\mid$ and $k\overrightarrow{a}+\frac{1}{2}\overrightarrow{a}$ is parallel to $\overrightarrow{a}$ holds true are_________.
cbse
class12
ch10
q37
p219
exemplar
medium
math
sec-a
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The vectors $\overrightarrow{a}=3\hat i+2\hat j+2\hat k$ and $\overrightarrow{b}=-\hat i+2\hat k$ are the adjacent sides of a parallelogram .The acute angle between its diagonals is__________.
cbse
class12
ch10
q36
p219
fitb
exemplar
medium
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{r}.\overrightarrow{a}=0,\overrightarrow{r}.\overrightarrow{b}=0$ and $\overrightarrow{r}.\overrightarrow{c}=0$ for some non-zero vector $\overrightarrow{r}$,then the value of $\overrightarrow{a}.(\overrightarrow{b}\times\overrightarrow{c})$ is___________.
cbse
class12
ch10
q35
p219
exemplar
medium
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The vector $\overrightarrow{a}+\overrightarrow{b}$ bisects the angle between the non-collinear vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ if__________.
cbse
class12
ch10
q34
p218
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The number of vectors of unit length perpendicular to the vectors $\overrightarrow{a}=2\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=\hat j+\hat k$ is
cbse
class12
ch10
q33
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\mid\overrightarrow{a}\mid=4$ and $-3\leq\:\lambda\leq 2$,then the range of $\mid\lambda\overrightarrow{a}\mid$ is
cbse
class12
ch10
q32
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors such that $\mid\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\mid=0$ and $\mid\overrightarrow{a}\mid=.2, \mid\overrightarrow{b}\mid=3,\mid\overrightarrow{c}\mid=5$,then value of $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}$ is
cbse
class12
ch10
q31
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Projection vector of $\overrightarrow{a}$ on $\overrightarrow{b}$ is
cbse
class12
ch10
q30
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are unit vectors such that$\mid\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\mid=0$,then the value of $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}$ is
cbse
class12
ch10
q29
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The vector $\hat i+\lambda\hat j+\hat k,\hat i+\hat j-\hat k$ and $3\hat i+6\hat j-5\hat k$ are coplanar if
cbse
class12
ch10
q28
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\mid\overrightarrow a\mid=10,\mid\overrightarrow b\mid=2$ and $\overrightarrow a.\overrightarrow b=12$,then value of $\mid\overrightarrow a\times\overrightarrow b\mid$ is
cbse
class12
ch10
q27
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
For any vector $\overrightarrow{a}$,the value of $(\overrightarrow{a}.\hat i)^2+ (\overrightarrow{a}.\hat j)^2+ (\overrightarrow{a}.\hat k)^2 $ is equal to
cbse
class12
ch10
q26
p218
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The vector from origin to the points $A$ and $B$ are $\overrightarrow{a}=2\hat i-3\hat j-2\hat k$ and $\overrightarrow{b}=2\hat i+3\hat j-\hat k,$ respectively,then the areqa of triangle $OAB$ is
cbse
class12
ch10
q25
p217
exemplar
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The value of $\lambda$ for which the vectors $3\hat i+6\hat j+\hat k $ and $ 2\hat i+4\hat j+\lambda\hat k$ are parallel is
cbse
class12
ch10
q24
p217
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find the value of $\lambda$ such that the vectors $\overrightarrow{a}=2\hat i+\lambda\hat j+\hat k$ and $\overrightarrow{b}=\hat i+2\hat j+3\hat k$ are orthogonal
cbse
class12
ch10
q23
p217
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The angle between two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with magnitudes $\sqrt 3$ and 4,respectively,and $\overrightarrow{a}.\overrightarrow{b}=2\sqrt 3$ is
cbse
class12
ch10
q22
p217
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The vector having initial and terminal points as $(2,5,0)$ and $(-3,7,4)$ respectively is
cbse
class12
ch10
q21
p217
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The position vector of the point which divides the join of points $2\overrightarrow{a}-3\overrightarrow{b}$ and $\overrightarrow{a}+\overrightarrow{b}$ in the ratio 3:1 is
cbse
class12
ch10
q20
p217
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The vector in the direction of the vector $\hat i+2\hat j+2\hat k$ that has magnitude $9$ is
cbse
class12
ch10
q19
p216
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a}=\hat i+\hat j+\hat k$ and $\overrightarrow{b}=\hat j-\hat k$,find a vector $\overrightarrow{c}$ such that $\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{b}$ and $\overrightarrow{a}.\overrightarrow{c}=3$.
cbse
class12
ch10
q18
p216
exemplar
medium
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Show that the area of the parallelogram whose diagonals are given by $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\mid \overrightarrow{a} \times \overrightarrow{b}\mid}{2}$.Also find the area of the parallelogram whose diagonals are $2\hat i+\hat j+\hat k$ and $\hat i+3\hat j+\hat k$.
cbse
class12
ch10
q17
p216
exemplar
easy
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
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