Recent questions in TN XII Math

Prove by the vector method , cos $(A+B)=$ cos $A$ cos $B$ - sin $A$ sin $B$

asked Apr 3, 2013 by poojasapani_1

1 answer

Prove by vector method , The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides.

asked Apr 3, 2013 by poojasapani_1

1 answer

Prove by vector method, The mid point of the hypotenuse of a right angled tringle is equidistant from its vertices.

asked Apr 3, 2013 by poojasapani_1

1 answer

Solve the equation $x^{4}-8x^{3}+24x^{2}-32x+20$ = 0 if $3+\mathit{i}$ is a root.

asked Apr 3, 2013 by geethradh

1 answer

Prove by the vector method If the diagonals of a parallelogram are equal than it is a rectangle.

asked Apr 3, 2013 by poojasapani_1

1 answer

Find the projection of $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{k}$ on $\overrightarrow{4i}-\overrightarrow{j}+\overrightarrow{2k}$

asked Apr 3, 2013 by poojasapani_1

1 answer

Find the projection of $\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{2k}$ on $\overrightarrow{2i}-\overrightarrow{j}+ \overrightarrow{5k}$

asked Apr 3, 2013 by poojasapani_1

1 answer

Find the projection of $\overrightarrow{i}-\overrightarrow{j}$ on $z$ axis

asked Apr 3, 2013 by poojasapani_1

1 answer

Show that the points whose position vectors $\overrightarrow{4i}-\overrightarrow{3j}+\overrightarrow{k}, \overrightarrow{2i}-\overrightarrow{4j}+\overrightarrow{5k} ,\overrightarrow{i}-\overrightarrow{j}$ form a right angled tringle.

asked Apr 3, 2013 by poojasapani_1

1 answer

Show that the vectors $\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{k},\overrightarrow{i}-\overrightarrow{3j}+\overrightarrow{5k}$ and $\overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{4k}$ form a right angled tringle.

asked Apr 3, 2013 by poojasapani_1

1 answer

Let $\overrightarrow{u},\overrightarrow{v}$ and $\overrightarrow{w}$ be vector such that $\overrightarrow{u}+\overrightarrow{v}+\overrightarrow{w}=\overrightarrow{0}.$ If $|\overrightarrow{u}|=3, |\overrightarrow{v}|=4$ and $|\overrightarrow{w}|=5$ than find $\overrightarrow{u}.\overrightarrow{v}+\overrightarrow{v}.\overrightarrow{w}+\overrightarrow{w}.\overrightarrow{u}$

asked Apr 3, 2013 by poojasapani_1

1 answer

If $|\overrightarrow{a}+\overrightarrow{b}|=60, |\overrightarrow{a}-\overrightarrow{b}|=40$ and $|\overrightarrow{b}|=46$ find $|\overrightarrow{a}|.$

asked Apr 3, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}\;,\overrightarrow{b}\;,\overrightarrow{c}$ are three mutually perpendicular unit vectors,than prove that $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\sqrt{3}$

asked Apr 3, 2013 by poojasapani_1

1 answer

If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is $\sqrt{3}$ .

asked Apr 3, 2013 by poojasapani_1

1 answer

Find the value of $m$ for which the vectors $\overrightarrow{a}=\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{9k}$ and $\overrightarrow{b}=\overrightarrow{i}+\overrightarrow{mj}+\overrightarrow{3k}$ are perpendicular

asked Apr 3, 2013 by poojasapani_1

1 answer

If $\hat{a}$ and $\hat{b}$ are unit vectors inclined at an angle $\theta$ ,than prove that cos $\Large\frac{\theta}{2}$ = $\Large\frac{1}{2}$ $|\hat{a}$ + $\hat{b}|$

asked Apr 3, 2013 by poojasapani_1

1 answer

If $\hat{a}$ and $\hat{b}$ are unit vectors inclined at an angle $\theta$ ,than prove that tan $\large\frac{\theta}{2}$ = $\large\frac{|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}$

asked Apr 2, 2013 by poojasapani_1

1 answer

Show that the vector $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is equally inclined with the coordinate axes.

asked Apr 2, 2013 by poojasapani_1

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

Find the value of $m$ for which the vectors $\overrightarrow{a}=\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{9k}$ and $\overrightarrow{b}=\overrightarrow{i}+\overrightarrow{mj}+\overrightarrow{3k}$ are parallel

asked Apr 2, 2013 by poojasapani_1

1 answer

Find $\lambda$ so that the vectors $\overrightarrow{2i}+\overrightarrow{\lambda\;j}+\overrightarrow{k}$ and $\overrightarrow{i}- \overrightarrow{2j} +\overrightarrow{k}$ are perpendicular to each other.

asked Apr 2, 2013 by poojasapani_1

1 answer

If arg $\left ( z-1 \right )$ = $\large\frac{\pi}{6}$ and arg $\left ( z+1 \right )$ = 2 $\large\frac{\pi}{3}$ then prove that $\left | z \right |=1$

asked Apr 2, 2013 by geethradh

1 answer

Express the following complex numbers in polar form. $1 - \mathit{i}$

asked Apr 2, 2013 by geethradh

1 answer

Express the following complex numbers in polar form. $-1 - \mathit{i}$

asked Apr 2, 2013 by geethradh

1 answer

Express the following complex number in polar form. $-1 + \mathit{i}\sqrt{3}$

asked Apr 2, 2013 by geethradh

1 answer

Express the following complex number in polar form. $2 + 2\sqrt{3}\mathit{i}$

asked Apr 2, 2013 by geethradh

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

If $\overrightarrow{a} =\overrightarrow{i} + \overrightarrow{j}+\overrightarrow{2k}\; and\; \overrightarrow{b}=\overrightarrow{3i} +\overrightarrow{2j}-\overrightarrow{k}$ find $(\overrightarrow{a}+\overrightarrow{3b}) . (\overrightarrow{2a}-\overrightarrow{b})$

asked Apr 2, 2013 by poojasapani_1

1 answer

Find $\overrightarrow{a} .\overrightarrow{b}$ when $\overrightarrow{a}=\overrightarrow{2i}+\overrightarrow{2j}-\overrightarrow{k}$ and $\overrightarrow{b} =\overrightarrow{6i}-\overrightarrow{3j}+\overrightarrow{2k}$

asked Apr 2, 2013 by poojasapani_1

1 answer

For what valus of $k$ , the system of equations $kx+y+z=1\;,x+ky+z=1\;,x+y+kz=1\;,$ have (i) unique solution (ii) more than one solution (iii) no solution.

asked Apr 2, 2013 by poojasapani_1

1 answer

Discuss the solutions of the system of equations for all values of $\lambda$ . $x+y+z=2\;,2x+y-2z=2\;,\lambda\;x+y+4z=2$

asked Apr 2, 2013 by poojasapani_1

1 answer

If $\left ( 1+\mathit{i} \right )\left ( 1+2\mathit{i} \right )\left ( 1+3\mathit{i} \right )... \left ( 1+\mathit{ni} \right )=\mathit{x+iy}$ , show that 2.5.10 ... $\left ( 1+n^{2} \right )$ = $x^{2}+y^{2}$

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

Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\sqrt{x^{2}+3x+8} + \left ( x+4 \right )\mathit{i} = \mathit{y}\left (2 + \mathit{i} \right )$

asked Apr 1, 2013 by geethradh

1 answer

Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\large\frac{\left ( 1+\mathit{i} \right )\mathit{x}-2\mathit{i}}{3+\mathit{i}} + \frac{\left ( 2-3\mathit{i} \right )\mathit{y}+\mathit{i}}{3-\mathit{i}} =$ $\mathit{i}$

asked Apr 1, 2013 by geethradh

1 answer

Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\left ( 1-\mathit{i} \right )\mathit{x} + \left ( 1+\mathit{i} \right )\mathit{y} = 1-3\mathit{i}$

asked Apr 1, 2013 by geethradh

1 answer

Find the least positive integer $\mathit{n}$ such that $\left ( \large\frac{1+\mathit{i}}{1-\mathit{i}} \right )^{\mathit{n}}$ $= 1$

asked Apr 1, 2013 by geethradh

1 answer

Find the real and imaginary parts of the following complex numbers: $\left ( 2+i \right )\left ( 3-2i \right )$

asked Apr 1, 2013 by geethradh

1 answer

Find the real and imaginary parts of the following complex numbers: $\large\frac{2+5i}{4-3i}$

asked Apr 1, 2013 by geethradh

1 answer

Find the real and imaginary parts of the following complex numbers: $\large\frac{1}{1+i}$

asked Apr 1, 2013 by geethradh

1 answer

Express the following in the standard form $a + ib$ : $\large\frac{i^{4}+i^{9}+i^{16}}{3-2i^{8}-i^{10}-i^{15}}$

asked Apr 1, 2013 by geethradh

1 answer

Express the following in the standard form $a + ib$ : $\left ( -3+i \right )\left ( 4-2i \right )$

asked Apr 1, 2013 by geethradh

1 answer

Express the following in the standard form $a+ib$ : $\large\frac{\left ( 1+i \right )\left ( 1-2i \right )}{1+3i}$

asked Apr 1, 2013 by geethradh

1 answer

Express the following in the standard form $a + ib$ : $\large\frac{2\left ( i-3 \right )}{\left ( 1+i \right )^{2}}$

asked Apr 1, 2013 by geethradh

1 answer

Express the following in the standard form $a + ib$ : $\frac{2(i-3)}{(1+i)^2}$

asked Apr 1, 2013 by balaji.thirumalai

0 answers

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y-z=1\;,2x+2y-2z=2\;,-3x-3y+3z=-3$

asked Mar 30, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x-4y+7z=14\;,3x+8y-2z=13\;,7x-8y+26z=5$

asked Mar 30, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y+z=7\;,x+2y+3z=18\;,y+2z=6$

asked Mar 30, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x-3y-8z=-10\;,3x+y-4z=0\;,2x+5y+6z-13=0$

asked Mar 30, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $4x+3y+6z=25\;,x+5y+7z=13\;,2x+9y+z=1$

asked Mar 30, 2013 by poojasapani_1

1 answer

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