Recent questions tagged tnstate

If $A (-1 , 4 , -3 ) $ is one end of a diameter $AB$ of the sphere $ x^{2}+y^{2}+z^{2}-3x-2y+2z-15=0$ than, Find the coordinates of $B$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Obtain the vector and cartesian equation of thesphere whose centre is $(1 , -1 , 1 )$ and radius is the same as that of the sphere $|\overrightarrow{r}-(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{2k})|=5.$

asked Apr 9, 2013 by poojasapani_1

1 answer

If $ \cos\;\alpha + \cos\;\beta + \cos\;\gamma = 0 = \sin \;\alpha + \sin \;\beta + \sin \;\gamma $, prove that $\sin 2\alpha + \sin 2\beta + \sin 2\gamma = 0$

asked Apr 8, 2013 by geethradh

1 answer

Find the vector and cartesian equationof the sphere on the join of the points $A$ and $B$ having position vectors $\overrightarrow{2i}+\overrightarrow{6j}-\overrightarrow{7k}$ and $-\overrightarrow{2i}+\overrightarrow{4j}-\overrightarrow{3k}$ respectively as a diameter . Find also the centre and radius of the sphere.

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector equation of a sphere with centre having position vector $\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{3k}$ and radius $4$ units. Also find the equation in cartesian form.

asked Apr 8, 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 angle between the line $\large\frac{x-2}{3}=\frac{y+1}{-1}=\frac{z-3}{-2}$and the plane $3x+4y+z+5=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

The planes $\overrightarrow{r} .(\overrightarrow{2i}+\lambda\overrightarrow{j}-\overrightarrow{3k})=10 $and $ \overrightarrow{r}. (\lambda\overrightarrow{i}+\overrightarrow{3j}+\overrightarrow{k})=5$ are perpendiculare find $\lambda$

asked Apr 8, 2013 by poojasapani_1

1 answer

Show that the following planes are at right angles.$\overrightarrow{r}(\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{k})=15$ and$ \overrightarrow{r}(\overrightarrow{i}-\overrightarrow{j}-\overrightarrow{3k})=3$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between following plane:$r=(3i+j-k)=7 $ and $r=(i+4j-2k)=10$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between following planes; $2x-3y+4z=1$ and $-x+y=4$

asked Apr 8, 2013 by poojasapani_1

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Find the angle between the followin planes: $2x+y-z=9 $and $x+2y+z=7$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the distane between the parallel planes $x-y+3z+5=0; 2x-2y+6z+7=0$

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 meeting point of the line $\overrightarrow{r}(\overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{3k}) + t(\overrightarrow{2i}-\overrightarrow{j}-\overrightarrow{k}) $ and the plane. $x-2y+3z+7=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the point of intersection of the line $\overrightarrow{r}=(\overrightarrow{j}-\overrightarrow{k})+s(\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{k})$ and $x z$ - plane.

asked Apr 8, 2013 by poojasapani_1

1 answer

Can u draw a plane through the given two lines? justify your answer.$\overrightarrow{r}(\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{4k})+t (\overrightarrow{2i}+\overrightarrow{3j} +\overrightarrow{6k})$ and $ r=(\overrightarrow{3i}+\overrightarrow{3j}-\overrightarrow{5k})+ s(-\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{8k})$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the equations of the plane which contains the two lines $\large\frac{x+1}{2}=\frac{y-2}{-3}=\frac{z-3}{4}$ and $\large\frac{x-4}{3}=\frac{y-1}{2}=z-8$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the cartesian form of following planes: $\overrightarrow{r}=(1+s+t) \overrightarrow{i}+(2-s+t)\overrightarrow{j}+(3-2s+2t)\overrightarrow{k}$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the cartesian form of following planes:$ \overrightarrow{r}=(s-2t) \overrightarrow{i}+(3-t)\overrightarrow{j}+(2s+t)\overrightarrow{k}$

asked Apr 8, 2013 by poojasapani_1

1 answer

Derive the equation of the plane in the intercept form.

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector cartesian equation of the plane passing through the points with position vectors $\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{2k}, \overrightarrow{2i}-\overrightarrow{2j}-\overrightarrow{2k},$ and $\overrightarrow{7i}+\overrightarrow{k}.$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector cartesian equation of the plane containing the line $\large\frac{x-2}{2}=\frac{y-2}{3}=\frac{z-1}{-2}$ and passing through the point $(-1 , 1 , -1 )$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane through the points $(1 , 2 , 3 )$and $(2 , 3 , 1 )$ perpendicular to the plane $ 3x-2y+4z-5=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane passing through the points $ A(1 , -2 , 3 )$ and $B(-1 , 2 , -1 )$ and is parallel to the line $ \large\frac{x-2}{2}=\frac{y+1}{3}=\frac{z-1}{4}.$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation to the plane through the point $(-1 , 3 , 2 ) $ and perpendicular to the planes $x+2y+2z=5$ and $3x+y+2z=8.$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane through the point $(1 , 3 , 2 ) $ and parallel to the lines $\large\frac{x+1}{2}=\frac{y+2}{-1}=\frac{z+3}{3}$ and parallel to the line $\large\frac{x-2}{1}=\frac{y+1}{2}=\frac{z+2}{2}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane containing the line $\Large\frac{x-2}{2}=\frac{y-2}{3}=\frac{z-1}{3}$ and parallel to the line $\Large\frac{x+1}{3}=\frac{y-1}{2}=\frac{z+1}{1}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane through the point $(2 , -1 , 4 )$ and parallel to the plane $\overrightarrow{r} . (\overrightarrow{4i}-\overrightarrow{12j}-\overrightarrow{3k})=7.$

asked Apr 7, 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

The foot of the perpendicular drawn from the origin to the plane is $(8 , -4 , 3 )$ find the equation of the plane.

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the length of the perpendicular frome the origin to the plane$\overrightarrow{r} . (\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{12k})=26$.

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the unit normal vectors to the plane $2x-y+2z=5$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of a plane which is at a distance of $18$ units from the origin and which is normal to the vector $\overrightarrow{2i}+\overrightarrow{7j}+\overrightarrow{8k}$

asked Apr 7, 2013 by poojasapani_1

1 answer

If the point $(\lambda , 0 , 3 ), (1 , 3 , -1 )$ and $(-5 , -3 , 7 )$ are collinear than find $\lambda$.

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 the shortest distance between the skew lines $\large\frac{x-6}{3}=\frac{y-7}{-1}=\frac{z-4}{1}$ and $\large\frac{x}{-3}=\frac{y+9}{2}=\frac{z-2}{4}$

asked Apr 7, 2013 by poojasapani_1

1 answer

Show that the lines $\large \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{3}$ and $\large\frac{x-2}{1}=\frac{y-1}{2}=\frac{-z-1}{1}$ intersect and find their point of intersection.

asked Apr 7, 2013 by poojasapani_1

1 answer

Show that the following two lines are skew lines: $\overrightarrow{r}=(\overrightarrow{3i}+\overrightarrow{5j}+\overrightarrow{7k})+ t (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{k})$ and $\overrightarrow{r}=(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}) + s (\overrightarrow{7i}-\overrightarrow{6j}+\overrightarrow{7k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the shortest distance between the parallel lines $\large\frac{x-1}{-1}=\frac{y}{3}=\frac{z+3}{2} $ and $\large\frac{x-3}{-1}=\frac{y+1}{3}=\frac{z-1}{2} $

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the shortest distance between the parallel lines $\overrightarrow{r}=(\overrightarrow{2i}-\overrightarrow{j}-\overrightarrow{k}) + t (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k})$ and $\overrightarrow{r}=(\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{k}) + s (\overrightarrow{i}-\overrightarrow{2j}+\overrightarrow{3k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the angle between the lines $\overrightarrow{r}=\overrightarrow{5i}-\overrightarrow{7j}+\mu (-\overrightarrow{i}+\overrightarrow{4j}+\overrightarrow{2k}) \overrightarrow{r}=-\overrightarrow{2i}+\overrightarrow{k}+\lambda (\overrightarrow{3i}+\overrightarrow{4k})$

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the angle between the following lines. $\large\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-4}{6}$ and $ x+1=\large\frac{y+2}{2}=\frac{z-4}{2}$

asked Apr 6, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation of the line joining the points $(1 , -2 , 1 )$ and $(0 , -2 , 3 ).$

asked Apr 6, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation of the line through the point $(3 , -4 , -2 )$ and parallel to vector $\overrightarrow{9i} +\overrightarrow{6j} +\overrightarrow{2k}$.

asked Apr 6, 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

A vector $\overrightarrow{r}$ has length $35\sqrt{2}$ and direction ratios $(3 , 4 , 5 ),$ Find the direction consines and components of $\overrightarrow{r}$.

asked Apr 6, 2013 by poojasapani_1

1 answer

What are the d . c . s of the vector equally inclined to the axes?

asked Apr 6, 2013 by poojasapani_1

1 answer

Can a vector have direction angles $45^{\circ}, 60^{\circ}, 120^{\circ}$?

asked Apr 6, 2013 by poojasapani_1

1 answer

Can a vector have direction angles $30^{\circ},45^{\circ},60^{\circ}$?

asked Apr 6, 2013 by poojasapani_1

1 answer

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