Recent questions tagged class12

In a rt. angled $\Delta$ $ABC$, the hypotenuse $|\overrightarrow {AB}|=p$,then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}=?$

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

Area of a parallelogram with adjacent sides $\overrightarrow a=\overrightarrow p+2\overrightarrow q,$ and $\overrightarrow b=2\overrightarrow p+\overrightarrow q$, where $\overrightarrow p,\overrightarrow q$ are unit vectors with angle $\large\frac{\pi}{6}$ between them is ?

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

$|\overrightarrow a|=3,\:|\overrightarrow b|=4,\:|\overrightarrow a+\overrightarrow b|=5,$ then $|\overrightarrow a-\overrightarrow b|=?$

asked Nov 6, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i-\hat j+2\hat k, \:\:\overrightarrow b=2\hat i+4\hat j+\hat k\:\:and\:\:\overrightarrow c=\lambda \hat i+\hat j+\mu k$ are mutually $\perp$ then $(\lambda,\mu)=?$

asked Nov 5, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\;and\:\overrightarrow b$ are unit vectors and if vectors $\overrightarrow c=\overrightarrow a+2\overrightarrow b$ and $\overrightarrow d=5\overrightarrow a-4\overrightarrow b$ are $\perp$ to each other, then the angle between $\overrightarrow a\;and\:\overrightarrow b$ is ?

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a$ and $\overrightarrow b$ are such that $|\overrightarrow a+\overrightarrow b|=\sqrt {29}$ and $\overrightarrow a\times (2\hat i+3\hat j+4\hat k)=(2\hat i+3\hat j+4\hat k) \times \overrightarrow b$, then the possible value of $(\overrightarrow a+\overrightarrow b).(-7\hat i+2\hat j+3\hat k)=?$

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

The vector $\hat i+x\hat j+3\hat k$ is rotated about angle $\theta$ and is doubled in magnitude, then it becomes $4\hat i+(4x-2)\hat j+2\hat k$. The value of $x=?$

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i-\hat k,\:\overrightarrow b=x\hat i+\hat j+(1-x)\hat k\:and\:\overrightarrow c=y\hat i+x\hat j+(1+x-y)\hat k$, then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$ depends on?

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i-\hat k,\:\overrightarrow b=x\hat i+\hat j+(1-x)\hat k\:and\:\overrightarrow c=y\hat i+x\hat j+(1+x-y)\hat k$, then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$ depends on?

asked Nov 4, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors and $\theta$ is angle between them then $\large\frac{1}{2}$$|\overrightarrow a-\overrightarrow b|$=?

asked Nov 1, 2013 by rvidyagovindarajan_1

1 answer

$(\overrightarrow a+\overrightarrow b+\overrightarrow c).[(\overrightarrow a+\overrightarrow b)\times (\overrightarrow a+\overrightarrow c)]=?$

asked Nov 1, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow p,\overrightarrow q$ are non collinear vectors, then $[\hat i\:\overrightarrow p\:\overrightarrow q]\hat i+[\hat j\:\overrightarrow p\:\overrightarrow q]\hat j+[\hat k\:\overrightarrow p\:\overrightarrow q]\hat k$=?

asked Nov 1, 2013 by rvidyagovindarajan_1

1 answer

The angle between the diagonals of a parallelogram $ABCD$, where $\overrightarrow {AB}=3\hat i-2\hat j+2\hat k$ and $\overrightarrow {BC}=-\hat i-2\hat k$ is?

asked Nov 1, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=2,\:|\overrightarrow b|=3\:and\:|\overrightarrow c|=4$ and $\overrightarrow a+\overrightarrow b+\overrightarrow c=\overrightarrow O$, then $\overrightarrow b.\overrightarrow c+\overrightarrow c.\overrightarrow a+\overrightarrow a.\overrightarrow b=?$

asked Oct 30, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\:\overrightarrow b\:and\:\overrightarrow c$ are mutually $\perp$ vectors of equal magnitude then the angle $\theta$ made by $\overrightarrow a+\overrightarrow b+\overrightarrow c$with any one of these 3 vectors is ?

asked Oct 30, 2013 by rvidyagovindarajan_1

1 answer

The sides of a parallelogram are given by vectors $2\hat i+4\hat j-5\hat k$ and $\hat i+2\hat j+3\hat k$. Unit vector along one of the diagonals is given by ?

asked Oct 30, 2013 by rvidyagovindarajan_1

1 answer

The points with position vectors $60\hat i+3\hat j,\:70\hat i-8\hat j\:and\:a\hat i-52\hat j$ are collinear if $a=?$

asked Oct 29, 2013 by rvidyagovindarajan_1

1 answer

$[\overrightarrow a\:\:\overrightarrow b\:\:\overrightarrow a\times\overrightarrow b]$=?

asked Oct 29, 2013 by rvidyagovindarajan_1

1 answer

If $ABCD$ is a Rhombus, with position vectors of vertices,$\overrightarrow {OA},\:\overrightarrow {OB},\:\overrightarrow {OC}\:and\:\overrightarrow {OD}$, then $\overrightarrow {OA}+\overrightarrow {OB}+\overrightarrow {OC}+\overrightarrow {OD}=?$

asked Oct 29, 2013 by rvidyagovindarajan_1

1 answer

$(\hat i\:\hat j\:\hat k)+(\hat j\:\hat k\: \hat i)+(\hat k\:\hat j\:\hat i)=?$

asked Oct 28, 2013 by rvidyagovindarajan_1

1 answer

If $\theta$ is the angle between the vectors $\overrightarrow a$ and $\overrightarrow b$, and $ |\overrightarrow a.\overrightarrow b|=|\overrightarrow a\times\overrightarrow b|$, then $\theta$=?

asked Oct 28, 2013 by rvidyagovindarajan_1

1 answer

If $|\overrightarrow a|=2,\:|\overrightarrow b|= 3$ and $\overrightarrow a.\overrightarrow b=4$, then $|\overrightarrow a-\overrightarrow b|$=?

asked Oct 28, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a$ is a non zero vector with magnitude $a$ and $\lambda a$ is a non zero scalar then $\lambda\overrightarrow a$ is a unit vector if $\lambda=?$

asked Oct 28, 2013 by rvidyagovindarajan_1

1 answer

Which of one of the following is a vector?

asked Oct 28, 2013 by rvidyagovindarajan_1

1 answer

Find all possible values of $p$ and $q$ for which $\cos^{-1}\sqrt p+\cos^{-1}\sqrt{1-p}=\large\frac{3\pi}{4}$

asked Oct 21, 2013 by sreemathi.v

1 answer

Let $a,b,c$ be positive real numbers .Let $\theta=\tan^{-1}\sqrt{\large\frac{a(a+b+c)}{bc}}+$$\tan^{-1}\sqrt{\large\frac{b(a+b+c)}{ca}}$$+\tan^{-1}\sqrt{\large\frac{c(a+b+c)}{ab}}$.Then $\tan\theta$

asked Oct 21, 2013 by sreemathi.v

1 answer

If $x=\sin^{14}\theta+\cos ^{20}\theta$,then for all $\theta\in R$

asked Oct 18, 2013 by sreemathi.v

1 answer

Evaluate : $\sin^{-1}\large\frac{4}{5}$$+\sin^{-1}\large\frac{5}{13}$$+\sin^{-1}\large\frac{16}{65}$

asked Oct 17, 2013 by sreemathi.v

1 answer

Find the value of $\tan\big[\large\frac{1}{2}$$\big(\sin^{-1}\large\frac{2x}{1+x^2}+$$\cos^{-1}\large\frac{1-y^2}{1+y^2}\big)\big],$$\mid x\mid < 1,y > 0$ and $xy <1$

asked Oct 17, 2013 by sreemathi.v

1 answer

Evaluate : $\tan\big[\large\frac{1}{2}$$\cos^{-1}\large\frac{\sqrt 5}{3}\big]$

asked Oct 17, 2013 by sreemathi.v

1 answer

If $f: R \to C $ is defined by $f(x)=e^{2ix}$ for $x \in R$ then, f is (Where C denotes the set of all complex numbers)

asked Oct 16, 2013 by meena.p

1 answer

$\cot^{-1}\big(\sqrt{\cos\alpha}-\tan^{-1}(\sqrt{\cos\alpha}\big)=x$ then $\sin x=?$

asked Oct 16, 2013 by sreemathi.v

1 answer

Find $\cos\tan^{-1}\sin\cot^{-1}x$

asked Oct 16, 2013 by sreemathi.v

1 answer

The value of $\cot\sum\limits_{n=1}^{23}\cot^{-1}\big(1+\sum\limits_{k=1}^n 2k\big)$ is

asked Oct 16, 2013 by sreemathi.v

1 answer