Recent questions tagged q5

Find the centre and radius of the following spheres : $| \overrightarrow{r}-(\overrightarrow(2i)-\overrightarrow(j)+\overrightarrow{4k})|=5$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the angle between the line $\overrightarrow{r}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{3k}+\lambda(\overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{k})$ and the plane $\overrightarrow{r}.(\overrightarrow{i}+\overrightarrow{j})=1.$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the distance from the origin to the plane $\overrightarrow{r}=(\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{5j})=7$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the equation of the plane through the point whose $p.v. $ is $\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{k}$ and perpendicular to the vector $\overrightarrow{4i}+\overrightarrow{2j}-\overrightarrow{3k}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Show that $(2 , -1 ,3 ),(1 ,-1, 0 )$ and $(3, -1, 6 )$ are collinear.

asked Apr 7, 2013 by poojasapani_1

1 answer

Find direction consines of the line joinong $(2 , -3 , 1 )$and $(3 , 1 , -2 ).$

asked Apr 6, 2013 by poojasapani_1

1 answer

if $\ \overrightarrow{a}= \overrightarrow{2i}+ \overrightarrow{3j}- \overrightarrow{k} , \overrightarrow{b}= -\overrightarrow{2i}+ \overrightarrow{5k}, \overrightarrow{c}= \overrightarrow{j}- \overrightarrow{3k}. $ Verify that $ \overrightarrow{a}\times ( \overrightarrow{b}\times \overrightarrow{c})= (\overrightarrow{a}. \overrightarrow{c}) \overrightarrow{b}- (\overrightarrow{a}. \overrightarrow{b})c$

asked Apr 5, 2013 by poojasapani_1

1 answer

Prove by the vector method, thet the parallelogram on the same base and between the same parallels are equal in area.

asked Apr 5, 2013 by poojasapani_1

1 answer

Find the angle between two vectors $\overrightarrow{a} $ and $\overrightarrow{b} $ if $|\overrightarrow{a} \times \overrightarrow{b}|=\overrightarrow{a}.\overrightarrow{b}$

asked Apr 4, 2013 by poojasapani_1

1 answer

Find the work done by the force $f=\overrightarrow{2i} + \overrightarrow{j}+\overrightarrow{k}$ acting on particle, if the particle is displaced from the point with position vector $\overrightarrow{2i}+ \overrightarrow{2j}+ \overrightarrow{2k}$ to the point with the position vector $\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{5k}$ .

asked Apr 4, 2013 by poojasapani_1

1 answer

Find the value of x if : $ \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} x & 3 \\ 2x & 5 \end{bmatrix} $

asked Apr 2, 2013 by sreemathi.v

1 answer

Find the angles which the vector $\overrightarrow{i}-\overrightarrow{j}+\sqrt{2}\overrightarrow{k}$ makes with the coordinate axes.

asked Apr 2, 2013 by poojasapani_1

1 answer

Prove that the points representing the complex numbers $\left ( 7+5\mathit{i} \right )$, $\left ( 5+2\mathit{i} \right )$, $\left ( 4+7\mathit{i} \right )$ and $\left ( 2+4\mathit{i} \right )$ form a parallelogram. (Plot the points and use midpoint formula).

asked Apr 2, 2013 by geethradh

1 answer

For what values of $\mathit{x}$ and $\mathit{y}$, the numbers $-3+\mathit{ix^{2}y}$ and $\mathit{x^{2}}+y+4\mathit{i}$ are complex conjugate of each other$?$

asked Apr 1, 2013 by geethradh

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

Find the rank of the following matrix :$\begin{bmatrix} 1 & 2 & -1 &3 \\2 & 4 & 1 &-2 \\3 & 6 & 3 &-7 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation$\;x-3y-8z+10=0\;,3x+y=4\;,2x+5y+6z=13$

asked Mar 29, 2013 by poojasapani_1

1 answer

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that$(AB)^{T}=B^{T}A^{T}$

asked Mar 28, 2013 by poojasapani_1

1 answer

If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$ and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that $(AB)^{-1}=B^{-1}A^{-1}$

asked Mar 28, 2013 by poojasapani_1

1 answer

Write the differential equation representing the family of curves y=mx,where m is an arbitrary constant.

asked Mar 20, 2013 by sreemathi.v

1 answer

Write the value of $\tan^{-1}\begin{bmatrix}2\sin\bigg(2\cos^{-1}\frac{\sqrt 3}{2}\bigg)\end{bmatrix}$

asked Mar 20, 2013 by sreemathi.v

1 answer

Write the principal value of $\tan^{-1}(\sqrt 3)-cot^{-1}(-\sqrt 3).$

asked Mar 20, 2013 by sreemathi.v

1 answer

State with reason whether following functions have inverse: (ii) $g: \{ 5,6,7,8\} \to \{1,2,3,4\}$ with $g= \{(5,4),(6,3),(7,4),(8,2)\}$

asked Mar 19, 2013 by balaji.thirumalai

1 answer

State with reason whether following functions have inverses: (i) $ f: \{ 1,2,3,4,\} \to \{10\}$ with $ f= \{(1,10),(2,10),(3,10), (4,10)\}$

asked Mar 19, 2013 by balaji.thirumalai

1 answer

Evaluate the determinants: $ \begin{vmatrix} 2&-1&2 \\ 0&2&-1 \\3&-5&0 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Evaluate the determinants: $ \begin{vmatrix} 0&1&2 \\ -1&0&3 \\-2&3&0 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

Evaluate the determinants: $ \begin{vmatrix} 3&-4&5 \\ 1&1&-2 \\2&3&1 \end{vmatrix}$

asked Mar 6, 2013 by sreemathi.v

1 answer

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (ii) } A = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix} \text{ , } B = \begin{bmatrix} 1 & 5 & 7 \end{bmatrix} $$

asked Mar 5, 2013 by balaji.thirumalai

1 answer

Write the value of the determinants \[ \begin{vmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x \end{vmatrix} \]

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Differentiate with respect to x. $( \sec(\tan(\sqrt x)))$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find the cofactor of $ a_{12}$ in the following \[ \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}\]

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the value of x: $\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} x & 3 \\ 2x & 5 \end{bmatrix}$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Evaluate : $ 2\begin{vmatrix} 7 & -2 \\ -10 & 5 \end{vmatrix} $

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find the value of x if $ \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix}$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Differentiate $ cos(sin\: x)$ with respect to x.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix} $ then show that | 2A | = 4| A |

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, solve the following for x : $\begin{vmatrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{vmatrix} = 0 $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

A man fires 4 bullets on a thief. The probability that the thief will be killed by one bullet is 0.6. Find the probability that the thief is still alive.

asked Feb 5, 2013 by meena.p

0 answers

If a matrix has 5 elements, write all possible orders it can have.

asked Feb 5, 2013 by thanvigandhi_1

1 answer

A farmer has a supply of chemical fertilizer of type I which contains 10% nitrogen and 6% phosphoric acid and type II fertilizer which contains 5% nitrogen and 10% phosphoric acid. After testing the soil conditions of a field, it is found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for a good crop. The fertilizer type I costs Rs.2.00 per kg and type II costs Rs.3.00 per kg. How many kilograms of each fertilizer should be used to meet the requirement and the cost be minimum.

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the plane passing through the point (1,6,3) and perpendicular to the plane 2x+3y-z = 7

asked Feb 5, 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

Show that $ Ax^2+By^2=1$ is a solution of the diff. equation. $ x\bigg[y\bigg(\Large\frac{d^2y}{dx^2}\bigg)+\bigg(\frac{dy}{dx}\bigg)^2\bigg]=y \frac{dy}{dx}$

asked Feb 4, 2013 by meena.p

0 answers

Show that the area enclosed by the circle $ x^2+y^2=64a^2$ and the parabola $y^2=12ax$ is $ a^2 \bigg(\frac{16}{\sqrt 3}+\large\frac {64\pi}{\sqrt 3}\bigg)$

asked Feb 4, 2013 by meena.p

1 answer

write $ A^{-1} $ for $ A = \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Evaluate the determinant $ \begin{bmatrix} cos \theta & -sin \theta \\ sin \theta & cos \theta \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

If A is a square matrix satisfying $ A^2=1$, then what is the inverse of A?

asked Feb 3, 2013 by thanvigandhi_1

0 answers

If $ A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} $ and A + A' = I, then find the value of $ \theta $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Find a, for which $ f(x) = x^2-2ax+6$ is strictly increasing when x > 0.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Write a value of $ \int \large\frac{1-\tan x}{x+\log\cos\: x}$$ dx $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

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