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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
If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ represent the vertices of a triangle,then show that $\frac{1}{2}\mid\overrightarrow{b}\times\overrightarrow{c}+\overrightarrow{c}\times\overrightarrow{a}+\overrightarrow{a}\times\overrightarrow{b}\mid$ gives the vector area of the triangle .Hence deduce the condition that the three points $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are collinear.Also find the unit vector normal to the plane of the triangle.
cbse
class12
ch10
q16
p216
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Prove that in any triangle ABC,$ cos A=\large \frac{b^2+c^2-a^2}{2bc}$,$where \overrightarrow{a},\overrightarrow{b} and \overrightarrow{c}$ are the vectors of sides BC, CA and AB respectively.
cbse
class12
ch10
q15
p216
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Using vectors,prove that the parallelogram on the same base and between the same parallels are equal in area.
cbse
class12
ch10
q14
p216
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Using vectors,find the area of the triangle ABC with vertices $A(1,2,3),B(2,-1,4)$ and $C(4,5,-1).$
cbse
class12
ch10
q13
p216
exemplar
easy
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $A,B,C,D$ are the points with position vectors $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k},2\overrightarrow{i}-3\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{i}+\overrightarrow{k},$ respectively ,find the projection of $\overrightarrow{AB}$ along $\overrightarrow{CD}.$
cbse
class12
ch10
q12
p216
short-answer
exemplar
easy
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find the sine of the angle between the vectors $\overrightarrow{a}=3\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=-2\hat i+2\hat j+4\hat k.$
cbse
class12
ch10
q11
p215
exemplar
easy
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0,$show that $\overrightarrow{a} \times \overrightarrow{b}=\overrightarrow{b} \times \overrightarrow{c} =\overrightarrow{c} \times \overrightarrow{a}$.Interpret the result geometrically?
cbse
class12
ch10
q10
p215
short-answer
exemplar
math
sec-b
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find the angle between the vectors $2\hat i\;-\hat j\;-\hat k$ and $3\hat i\;+4\hat j\;+\hat k$.
cbse
class12
ch10
q9
p215
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
FInd a vector of magnitude 6 ,which is perpendicular to both the vectors $2\hat i-\hat j+2\hat k$ and $4\hat i-\hat j+3\hat k.$
cbse
class12
ch10
q8
p215
exemplar
easy
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
A vector $\overrightarrow{r}$ has magnitude 14 and direction ratios 2,3,-6.Find the direction cosines and components of $\overrightarrow{r}$,given that $\overrightarrow{r}$ makes an acute angle with x-axis.
cbse
class12
ch10
q7
p215
exemplar
medium
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
A vector $\overrightarrow{r}$ is inclined at equal angles to the three axes.If the magnitude of $\overrightarrow{r}$ is $2\sqrt 3$ units,find $\overrightarrow{r}.$
cbse
class12
ch10
q6
p215
short-answer
exemplar
easy
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Using vectors,find the value of k such that the points $(k,-10,3),(1,-1,3)$ and $(3,5.3)$ are collinear.
cbse
class12
ch10
q5
p215
exemplar
medium
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a}$ and $\overrightarrow{b}$ are the position vectors of $A$ and $B$,respectively,find the position vector of a point $C$ in $BA$ produced such that $BC=1.5BA$.
cbse
class12
ch10
q4
p215
exemplar
medium
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find a unit vector in the direction of $\overrightarrow{PQ},$where $P$ and $Q$ have co-ordinates $(5,0,8)$ and $(3,3,2)$,respectively.
cbse
class12
ch10
q3
p215
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a}=\hat i-\hat j+2\hat k\;and\;\overrightarrow{b}=2\hat i-\hat j-2\hat k,$then find the unit vector in the direction of $ 6 \overrightarrow{b} $
cbse
class12
ch10
q2
p215
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Find the unit vector in the direction of sum of vectors $\overrightarrow{a}=2\hat i+\hat j+\hat k\;and\;\overrightarrow{b}=2\hat j-\hat k$
cbse
class12
ch10
q1
p215
exemplar
easy
sec-a
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Represent graphically a displacement of 40 km, 30° east of north.
cbse
class12
bookproblem
ch10
ex-1
q1
p428
sec-a
easy
math
asked
Dec 7, 2012
by
thanvigandhi_1
1
answer
Classify the following measures as scalars and vectors. $(i)\;10\: kg$
cbse
class12
bookproblem
ch10
ex-1
q2
q2-1
p428
sec-a
easy
math
asked
Dec 7, 2012
by
thanvigandhi_1
1
answer
Classify the following as scalar and vector quantities. $ (i)\; $time period.
cbse
class12
bookproblem
ch10
ex-1
q3
q3-1
p428
sec-a
easy
math
asked
Dec 7, 2012
by
thanvigandhi_1
1
answer
In Fig 10.6 (a square), identify the following vectors. \[(i)\; Coinitial\qquad (ii)\; Equal\qquad (iii)\; Collinear\; but\; not\; equal \]
cbse
class12
bookproblem
ch10
ex-1
q4
p428
sec-a
easy
math
asked
Dec 7, 2012
by
thanvigandhi_1
1
answer
Answer the following as true or false. $\\(i)\; \overrightarrow a$ and -$\overrightarrow a$ are collinear.
cbse
class12
bookproblem
ch10
ex-1
q5
q5-1
p428
sec-a
easy
math
asked
Dec 7, 2012
by
thanvigandhi_1
1
answer
Compute the magnitude of the following vectors: $(i)\;\overrightarrow a = \hat i + \hat j + \hat k$
cbse
class12
bookproblem
ch10
sec2
q1
q1-1
p440
sec-a
easy
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Write two different vectors having same magnitude.
cbse
class12
bookproblem
ch10
sec2
q2
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Write two different vectors having same direction.
cbse
class12
bookproblem
ch10
sec2
q3
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the values of $x$ and $y$ so that the vectors $2\hat i + 3\hat j$ and $x\hat i + y\hat j$ are equal.
cbse
class12
bookproblem
ch10
sec2
q4
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the scalar and vector components of the vector with initial point $(2, 1)$ and terminal point $(– 5, 7).$
cbse
class12
bookproblem
ch10
sec2
q5
p440
medium
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the sum of the vectors $\overrightarrow a=\hat i − 2\hat j + \hat k, \overrightarrow b=−2\hat i + 4\hat j + 5\hat k$ and $\overrightarrow c = \hat i − 6\hat j – 7\hat k$ .
cbse
class12
bookproblem
ch10
sec2
q6
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the unit vector in the direction of the vector $ \overrightarrow a = \hat i + \hat j + 2\hat k$ .
cbse
class12
bookproblem
ch10
sec2
q7
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the unit vector in the direction of vector $ \overline{PQ}$, where $P$ and $Q$ are the points $(1, 2, 3)$ and $(4, 5, 6)$ respectively.
cbse
class12
bookproblem
ch10
sec2
q8
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
For given vectors, $ \overrightarrow a=2\hat i − \hat j + 2\hat k$ and $ \overrightarrow b=−\hat i + \hat j − \hat k$, find the unit vector in the direction of the vector $ \overrightarrow a +\overrightarrow b.$
cbse
class12
bookproblem
ch10
sec2
q9
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find a vector in the direction of vector $5\hat i − \hat j + 2\hat k$ which has magnitude $8$ units.
cbse
class12
bookproblem
ch10
sec2
q10
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Show that the vectors \(2\hat i − 3\hat j + 4\hat k\) and \(− 4\hat i + 6\hat j − 8\hat k\) are collinear.
class12
bookproblem
ch10
sec2
q11
p440
easy
sec-a
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the direction cosines of the vector $\hat i + 2\hat j + 3\hat k$
cbse
class12
bookproblem
ch10
sec2
q12
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the direction cosines of the vector joining the points $A(1, 2, –3)$ and $B(–1, –2, 1),$ directed from $A$ to $B$.
cbse
class12
bookproblem
ch10
sec2
q13
p440
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Show that the vector $ \hat i + \hat j + \hat k$ is equally inclined to the axes OX, OY and OZ.
cbse
class12
bookproblem
ch10
sec2
q14
p440
medium
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the position vector of a point $R$ which divides the line joining two points $P$ and $Q$ whose position vectors are $ \hat i + 2\hat j − \hat k$ and $ – \hat i + \hat j + \hat k$ respectively, in the ratio $2 : 1$ internally
cbse
class12
bookproblem
ch10
sec2
q15
q15-1
p440
medium
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the position vector of the mid point of the vector joining the points $P(2, 3, 4)$ and $Q(4, 1, –2)$.
cbse
class12
bookproblem
ch10
sec2
q16
p441
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Show that the points A, B and C with position vectors, \( \overrightarrow a = 3\hat i − 4\hat j − 4\hat k, \overrightarrow b = 2\hat i − \hat j + \hat k\) and \( \overrightarrow c = \hat i − 3\hat j − 5\hat k\) , respectively form the vertices of a right angled triangle.
cbse
class12
bookproblem
ch10
sec2
q17
p441
medium
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
If $\overrightarrow a$ and $ \overrightarrow b$ are two collinear vectors, then which of the following are incorrect:
cbse
class12
bookproblem
ch10
sec2
q19
p441
sec-a
easy
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the angle between two vectors \( \overrightarrow a\) and \( \overrightarrow b\) with magnitudes \( \sqrt 3\) and \(2\) , respectively having \( \overrightarrow a . \overrightarrow b = \sqrt 6.\)
cbse
class12
bookproblem
ch10
sec3
q1
p447
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the angle between the vectors $\hat i - 2\hat j + 3\hat k$ and $ 3\hat i - 2\hat j + \hat k$
cbse
class12
bookproblem
ch10
sec3
q2
p477
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the projection of the vector $ \hat i − \hat j$ on the vector $ \hat i + \hat j $.
cbse
class12
bookproblem
ch10
sec3
q3
p447
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the projection of the vector $ \hat i + 3\hat j + 7\hat k$ on the vector $7\hat i − \hat j + 8\hat k$.
cbse
class12
bookproblem
ch10
sec3
q4
p447
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Show that each of the given three vectors is a unit vector: $ \large\frac{1}{7}$$ ( 2\hat i + 3\hat j + 6\hat k),\large\frac{1}{7}$$ ( 3\hat i - 6\hat j + 2\hat k), \large\frac{1}{7}$$ ( 6\hat i + 2\hat j - 3\hat k) $ Also, show that they are mutually perpendicular to each other.
cbse
class12
bookproblem
ch10
sec3
q5
p447
easy
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find $| \overrightarrow a |$ and $| \overrightarrow b |$ , if $(\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a − \overrightarrow b) = 8$ and $| \overrightarrow a |= 8 | \overrightarrow b |.$
cbse
class12
bookproblem
ch10
sec3
q6
p448
medium
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Evaluate the product $(3\overrightarrow a − 5\overrightarrow b) ⋅ (2\overrightarrow a + 7\overrightarrow b)$
cbse
class12
bookproblem
ch10
sec3
q7
p448
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find the magnitude of two vectors $ \overrightarrow a$ and $\overrightarrow b$ , having the same magnitude and such that the angle between them is $60^{\omicron}$ and their scalar product is $\large \frac{1}{2}$.
cbse
class12
bookproblem
ch10
sec3
q8
p448
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find $| \overrightarrow x |$, if for a unit vector $\overrightarrow a , (\overrightarrow x − \overrightarrow a) ⋅ (\overrightarrow x + \overrightarrow a) =12$.
cbse
class12
bookproblem
ch10
sec3
q9
p448
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
If $\overrightarrow a = 2\hat i + 2\hat j + 3\hat k,\: \overrightarrow b = − \hat i + 2\hat j + \hat k$ and $ \overrightarrow c = 3\hat i + \hat j$ are such that $\overrightarrow a + λ\overrightarrow b $ is perpendicular to $ \overrightarrow c $ , then find the value of $λ.$
cbse
class12
bookproblem
ch10
sec3
q10
p448
easy
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Show that $| \overrightarrow a | \overrightarrow b + | \overrightarrow b | \overrightarrow a$ is perpendicular to $| \overrightarrow a | \overrightarrow b - | \overrightarrow b | \overrightarrow a$, for any two nonzero vectors $\overrightarrow a$ and $\overrightarrow b$.
cbse
class12
bookproblem
ch10
sec3
q11
p448
easy
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
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