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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 a = 0$ and $ \overrightarrow a . \overrightarrow b = 0$, then what can be concluded about the vector $\overrightarrow b$?
cbse
class12
bookproblem
ch10
sec3
q12
p448
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
If $ \overrightarrow a, \overrightarrow b, \overrightarrow c, $are unit vectors such that $ \overrightarrow a + \overrightarrow b + \overrightarrow c = \overrightarrow 0$, find the value of $ \overrightarrow a ⋅ \overrightarrow b + \overrightarrow b ⋅ \overrightarrow c + \overrightarrow c ⋅ \overrightarrow a$.
cbse
class12
bookproblem
ch10
sec3
q13
p448
easy
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
If either vector \(\overrightarrow a = \overrightarrow 0\) or \(\overrightarrow b = \overrightarrow 0\), then \(\overrightarrow a . \overrightarrow b = 0\). But the converse need not be true. Justify your answer with an example.
cbse
class12
bookproblem
ch10
sec3
q14
p448
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
If the vertices $A, B, C$ of a triangle $ABC$ are $(1, 2, 3), (-1, 0, 0), (0, 1, 2)$ respectively, then find $ \angle ABC. \angle ABC$ is the angle between the vectors $ \overline {BA}$ and $\overline {BC}$.
cbse
class12
bookproblem
ch10
sec3
q15
p448
medium
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.
cbse
class12
bookproblem
ch10
sec3
q16
p448
easy
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Show that the vectors \(2\hat i - \hat j + \hat k, \: \hat i - 3\hat j - 5\hat k\) and \(3\hat i - 4\hat j - 4\hat k\) form the vertices of a right angled triangle.
cbse
class12
bookproblem
ch10
sec3
q17
p448
medium
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
If $\overrightarrow a$ is a nonzero vector of magnitude $" a "$ and $λ$ a nonzero scalar, then $λ \overrightarrow a$ is unit vector if
cbse
class12
bookproblem
ch10
sec3
q18
p448
easy
sec-a
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Find $| a × b |$, if $a = \hat i - 7\hat j + 7\hat k$ and $b = 3\hat i - 2\hat j + 2\hat k$
cbse
class12
bookproblem
ch10
sec4
q1
p454
medium
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Find a unit vector perpendicular to each of the vector \( \overrightarrow a + \overrightarrow b\) and \( \overrightarrow a - \overrightarrow b\), where \( \overrightarrow a = 3\hat i + 2\hat j + 2\hat k\) and \( \overrightarrow b = \hat i + 2\hat j - 2\hat k\)
cbse
class12
bookproblem
ch10
sec4
q2
p454
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
If a unit vector \(\overrightarrow a\) makes angles \( \frac{\large \pi}{\large 3} \) with \( \hat i, \frac{\large \pi}{\large 3} \) with \( \hat j\) and an acute angle \(θ\) with \( \hat k\) , then find \( θ \) and hence, the components of \( \overrightarrow a \) .
cbse
class12
bookproblem
ch10
sec4
q3
p454
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Show that $ ( \overrightarrow a - \overrightarrow b) \times ( \overrightarrow a + \overrightarrow b) = 2 ( \overrightarrow a \times \overrightarrow b) $
cbse
class12
bookproblem
ch10
sec4
q4
p454
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Find $λ$ and $μ$ if $ ( 2\hat i + 6\hat j + 27\hat k)\times (\hat i + λ\hat j + μ\hat k) = \overrightarrow 0$
cbse
class12
bookproblem
ch10
sec4
q5
p454
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Given that $\overrightarrow a . \overrightarrow b = 0$ and $ \overrightarrow a$ x $\overrightarrow b = \overrightarrow 0$ What can you conclude about the vectors $\overrightarrow a$ and $ \overrightarrow b$?
cbse
class12
bookproblem
ch10
sec4
q6
p454
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Let the vectors \( \overrightarrow a, \overrightarrow b, \overrightarrow c\) be given as \(a_1\hat i + a_2\hat j + a_3\hat k, \: b_1\hat i + b_2\hat j + b_3\hat k, \: c_1\hat i + c_2\hat j + c_3\hat k \). Then show that \( \overrightarrow a × (\overrightarrow b + \overrightarrow c) = \overrightarrow a × \overrightarrow b + \overrightarrow a × \overrightarrow c\)
cbse
class12
bookproblem
ch10
sec4
q7
p454
medium
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
If either $ \overrightarrow a = \overrightarrow 0 $ or $ \overrightarrow b = \overrightarrow 0 $ then $ \overrightarrow a × \overrightarrow b = \overrightarrow 0$. Is the converse true? Justify your answer with an example.
cbse
class12
bookproblem
ch10
sec4
q8
p454
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Find the area of the triangle with vertices $A(1, 1, 2), B(2, 3, 5)$ and $C(1, 5, 5)$.
cbse
class12
bookproblem
ch10
sec4
q9
p454
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Find the area of the parallelogram whose adjacent sides are determined by the vectors $ \overrightarrow a = \hat i - \hat j + 3\hat k$ and $\overrightarrow b = 2\hat i - 7 \hat j + \hat k$
cbse
class12
bookproblem
ch10
sec4
q10
p455
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Let the vectors $ \overrightarrow a$ and $ \overrightarrow b$ be such that $| \overrightarrow a | = 3$ and $ |\overrightarrow b | = \frac{\large \sqrt 2}{\large 3}$ , then $\overrightarrow a \times \overrightarrow b$ is a unit vector, if the angle between $ \overrightarrow a$ and $ \overrightarrow b$ is
cbse
class12
bookproblem
ch10
sec4
q11
p455
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Area of a rectangle having vertices $A, B, C$ and $D$ with position vectors $ -\hat i + \large\frac{1}{2}$$ \hat j + 4\hat k, \: \hat i +\large \frac{1}{2}$$ \hat j + 4\hat k, \: \hat i -\large \frac{1}{2}$$ \hat j + 4\hat k$ and $-\hat i -\large \frac{1}{2}$$ \hat j + 4\hat k$ respectively is
cbse
class12
bookproblem
ch10
sec4
q12
p455
medium
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Write down a unit vector in XY plane, making an angle of 30 degress with the positive direction of $x$ axis.
cbse
class12
bookproblem
ch10
misc
q1
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Find the scalar components and magnitude of the vector joining the points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$
cbse
class12
bookproblem
ch10
misc
q2
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.
cbse
class12
bookproblem
ch10
misc
q3
p458
difficult
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
If $\overrightarrow a = \overrightarrow b + \overrightarrow c$, then is it true that $| \overrightarrow a | = | \overrightarrow b | + | \overrightarrow c |$? Justify your answer.
cbse
class12
bookproblem
ch10
misc
q4
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Find the value of $x$ for which $x(\hat i + \hat j +\hat k)$ is a unit vector.
cbse
class12
bookproblem
ch10
misc
q5
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Find a vector of magnitude $5$ units, and parallel to the resultant of the vectors $\overrightarrow a = 2\hat i + 3 \hat j - \hat k$ and $\overrightarrow b = \hat i - 2\hat j + \hat k$
cbse
class12
bookproblem
ch10
misc
q6
p458
medium
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
If $\overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - \hat j + 3\hat k$ and $\overrightarrow c = \hat i - 2\hat j + \hat k$, find a unit vector parallel to the vector $2\overrightarrow a - \overrightarrow b + 3\overrightarrow c$
cbse
class12
bookproblem
ch10
misc
q7
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
cbse
class12
bookproblem
ch10
misc
q8
p458
easy
sec-b
math
asked
Dec 5, 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 \((2\overrightarrow a + \overrightarrow b)\) and \((\overrightarrow a - 3\overrightarrow b)\) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ
cbse
class12
bookproblem
ch10
misc
q9
p458
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
The two adjacent sides of a parallelogram are \(2\hat i - 4\hat j + 5\hat k\) and \( \hat i - 2\hat j - 3\hat k\) . Find the unit vector parallel to its diagonal. Also, find its area.
cbse
class12
bookproblem
ch10
misc
q10
p458
medium
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $ \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3} $
cbse
class12
bookproblem
ch10
misc
q11
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Let \(\overrightarrow a = \hat i + 4 \hat j + 2\hat k, \overrightarrow b = 3\hat i − 2 \hat j + 7\hat k \: and \: \overrightarrow c = 2\hat i − \hat j + 4\hat k \) . Find a vector \( \overrightarrow d\) which is perpendicular to both \(\overrightarrow a\) and \(\overrightarrow b\) , and \( \overrightarrow c ⋅ \overrightarrow d =15\)
cbse
class12
bookproblem
ch10
misc
q12
p348
difficult
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
The scalar product of the vector \(\hat i + \hat j + \hat k\) with a unit vector along the sum of vectors \(2\hat i + 4 \hat j − 5\hat k\) and \(λ\hat i + 2 \hat j + 3\hat k\) is equal to one. Find the value of \( λ.\)
cbse
class12
bookproblem
ch10
misc
q13
p458
sec-b
medium
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
If \( \overrightarrow a, \overrightarrow b, \overrightarrow c, \) are mutually perpendicular vectors of equal magnitudes, show that the vector \( \overrightarrow a + \overrightarrow b + \overrightarrow c\) is equally inclined to \( \overrightarrow a, \overrightarrow b and \overrightarrow c\).
cbse
class12
bookproblem
ch10
misc
q14
p458
difficult
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Prove that \( (\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a + \overrightarrow b) =| \overrightarrow a |^2 + |\overrightarrow b |^2\), if and only if \(\overrightarrow a,\: \overrightarrow b\) are perpendicular, given \(\overrightarrow a ≠ 0, \overrightarrow b ≠ 0\).
cbse
class12
bookproblem
ch10
misc
q15
p459
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer if θ is the angle between two vectors $\overrightarrow a$ and $ \overrightarrow b$, then $ \overrightarrow a \: . \: \overrightarrow b\ \: \geq 0$ only when
cbse
class12
bookproblem
ch10
misc
q16
p459
medium
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the following : let \( \overrightarrow a\) and \( \overrightarrow b\) be two unit vectors and θ is the angle between them. Then \( \overrightarrow a\ + \overrightarrow b\) is a unit vector if
cbse
class12
bookproblem
ch10
misc
q17
p459
easy
sec-b
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer if the value of $ \hat i.( \hat j\times \hat k)+ \hat j . (\hat i \times \hat k) +\hat k. (\hat i \times \hat j)$ is
cbse
class12
bookproblem
ch10
misc
q18
p459
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer if θ is the angle between any two vectors $\overrightarrow a$ and $\overrightarrow b$, then $| \overrightarrow a ⋅\overrightarrow b | \: = \: | \overrightarrow a \times\overrightarrow b |$ when θ is equal to
cbse
class12
bookproblem
ch10
misc
q19
p459
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
What is the value of $$\hat{i} (\hat{j}. \hat{k}) \hat{j} (\hat{i}. \hat{k}) \hat{k} (\hat{j}. \hat{i})?$$
cbse
class12
bookproblem
sec-a
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
If $\theta$ is the angle between any two vectors $ \overrightarrow{a} and \overrightarrow{b} ,$ then $|\overrightarrow{a}.\overrightarrow{b} | = | \overrightarrow{a} \times \overrightarrow{b} | $ when $\theta$ is equal to
bookproblem
class12
cbse
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
If θ is the angle between two vectors $$\overrightarrow{a} and \overrightarrow{b}$$ when is $$\overrightarrow{a} ⋅ \overrightarrow{b} ≥ 0$$
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Prove that $$(\overrightarrow{a} + \overrightarrow{b} ) ⋅ (\overrightarrow{a} + \overrightarrow{b} ) =| \overrightarrow{a} |2 + | \overrightarrow{b} |2$$ if and only if $$\overrightarrow{a} , \overrightarrow{b}$$ are perpendicular, given $$\overrightarrow{a} ≠ 0, \overrightarrow{b} ≠ 0$$
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
If $$\overrightarrow{a} ,\overrightarrow{b} , \overrightarrow{c}$$ are mutually perpendicular vectors of equal magnitudes, show that the vector $$\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}$$ is equally inclined to $$\overrightarrow{a}, \overrightarrow{b} and \overrightarrow{c} $$.
cbse
class12
ch10
sec-b
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Given $$\overrightarrow{a}, \overrightarrow{b} and \overrightarrow{c}$$ Find a vector $$\overrightarrow{d}$$ which is perpendicular to both $$\overrightarrow{a} and \overrightarrow{b}, and \overrightarrow{c} ⋅\overrightarrow{d} = 15$$
bookproblem
cbse
class12
sec-a
easy
ch10
math
asked
Nov 2, 2012
by
anonymous
0
answers
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $1 / \sqrt{3}, 1 / \sqrt{3}$ and $1 / \sqrt{3} $
cbse
class12
bookproblem
sec-a
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
The two adjacent sides of a parallelogram are given. Find the unit vector parallel to its diagonal. Also, find its area.
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find the position vector of a point tand show that P is the mod point of the line segment
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Show that the points A (1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
cbse
class12
bookproblem
sec-b
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find a unit vector parallel to the vector....
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find a vector of magnitude 5 units, and parallel to the resultant of the vectors
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
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