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Questions asked by thanvigandhi_1
Questions
5837
questions
1
answer selected
Find the value of the following:<br> $ tan^{-1} \bigg(tan \frac{7\pi}{6}\bigg)$
cbse
class12
bookproblem
ch2
misc
q2
p51
easy
sec-a
math
asked
Dec 10, 2012
1
answer
What does $ 2\sin^{-1} \frac{3}{5}$ reduce to
cbse
class12
bookproblem
ch2
misc
q3
p51
medium
sec-b
math
asked
Dec 10, 2012
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
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
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
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
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
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
1
answer
Write two different vectors having same magnitude.
cbse
class12
bookproblem
ch10
sec2
q2
p440
easy
sec-a
math
asked
Dec 6, 2012
1
answer
Write two different vectors having same direction.
cbse
class12
bookproblem
ch10
sec2
q3
p440
easy
sec-a
math
asked
Dec 6, 2012
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
1
answer
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
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
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
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
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
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
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
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
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
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
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
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
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
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
1
answer
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