Recent questions tagged tnstate

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