Recent questions tagged p35

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0}(\cos x)^{\large\frac{1}{x}}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to 0 +} x^{x}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim\limits_{x \to \large\frac{\pi}{2}\;-} (\tan x)^{\cos x}$

asked May 6, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $ 2x-y+z=2\;,6x-3y+3z=6\;,4x-2y+2z=4$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $x+2y+z=6\;,3x+3y-z=3\;,2x+y-2z=-3 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $3x+y-z=2\;,2x-y+2z=6\;,2x+y-2z=-2 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $ 2x+y-z=4\;,x+y-2z=0\;,3x+2y-3z=4 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $x+y+z=4\;,x-y+z=2\;,2x+y-z=1 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $4x+5y=9\;,8x+10y=18 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method: $2x+3y=5\;,4x+6y=12 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $3x+2y=5\;,x+3y=4$

asked Mar 29, 2013 by poojasapani_1

1 answer

Show that $2tan^{-1}(-3)=\frac{-\pi}{2}+tan^{-1}\bigg(\frac{-4}{3}\bigg)$

asked Feb 19, 2013 by sreemathi.v

1 answer

Find the value of $tan^{-1}\frac{-1}{\sqrt 3}+cot^{-1}\frac{1}{\sqrt 3}-tan^{-1}sin\frac{\pi}{2}$

asked Feb 19, 2013 by sreemathi.v

1 answer

Prove that \[cot(\frac{\pi}{4}-2cot^{-1}3)=7\]

asked Feb 19, 2013 by sreemathi.v

1 answer

Evaluate $cos\bigg(cos^{-1}\bigg(\frac{-\sqrt{3}}{2}\bigg)+\frac{\pi}{6}\bigg)$

asked Feb 19, 2013 by sreemathi.v

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.

asked Feb 4, 2013 by meena.p

1 answer

Prove that the area of a paralellogram with diagonals $\bar{a}\;and\;\bar{b}\;is\;\frac{1}{2}|\bar{a} \times \bar{b}|$

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}|$

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}$

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.

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}$?

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)

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\[(a)\;\cos \frac{\theta}{2}=\frac{1}{2}|\hat{a}+\hat{b}|\qquad(b)\;\tan \frac{\theta}{2}=\frac {|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}\]

asked Feb 4, 2013 by meena.p

1 answer

Prove that angle in a semi-circle is a right angle.

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$

asked Feb 4, 2013 by meena.p

1 answer

Prove Cauchy - Schawarz inequality : $(\bar{a}.\bar{b})^2\leq|\bar{a}|^2.|\bar{b}|^2$

asked Feb 4, 2013 by meena.p

0 answers

Prove the triangle inequality $\bigg|\overrightarrow{a}+\overrightarrow{b}\bigg|\leq\bigg|\overrightarrow{a}\bigg|+\bigg|\overrightarrow{b}\bigg|$

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}$

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}$

asked Feb 4, 2013 by meena.p

1 answer

Find the unit vector perpendicular to both the vectors\[\bar{a}=4\bar{i}-\bar{j}-3\bar{k}\;and\;\bar{b}=2\bar{i}+2\bar{j}-\bar{k}\]

asked Feb 4, 2013 by meena.p

0 answers

Find the value of $\tan^{-1}\bigg(\tan{\frac{2\pi}{3}}\bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the value of $\; \tan^{-1}\bigg(\tan{\frac{5\pi}{6}}\bigg)+\cos^{-1}\bigg(\cos{\frac{13\pi}{6}}\bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

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