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Questions >> CBSE XII >> Math >> Three Dimensional Geometry

If the lines $\overrightarrow r=(\hat i+2\hat j+3\hat k)+\lambda(3\hat i+2k\hat j-2\hat k)$ and $\overrightarrow r=(\hat i+2\hat j+3\hat k)+\mu(k\hat i+\hat j+5\hat k)$ are $\perp$ to one another then find the equation of the plane containing them.

asked Feb 4, 2014 by rvidyagovindarajan_1

1 answer

If O be the origin and the coordinates of P be (1, 2, – 3), then find the equation of the plane passing through P and perpendicular to OP.

asked Feb 3, 2014 by rvidyagovindarajan_1

1 answer

If the lines $\large\frac{2x-1} {-3} = \frac{y-2}{2k} = \frac{z-3}{2}$ and $\large\frac{x-1}{3k} = \frac{1-2y}{1} = \frac{z-6}{-5}$ are perpendicular, find the value of k.

asked Feb 3, 2014 by rvidyagovindarajan_1

1 answer

find the radius of cicular section of sphere x^2+y^2+z^2=49 by the plane 2x+3y-z-4(14)^1/2

asked Dec 28, 2013 by ankitclusters_1

0 answers

Are the points (2, 3, 4), (-1, -2, 1), (5, 8, 7) collinear?

asked Jul 20, 2013 by balaji.thirumalai

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane $(c)\;$ Point (2,3,-5);Plane $(x+2y-2z-9=0)$

asked Jun 4, 2013 by sreemathi.v

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane $(b)\;$ Point (3,-2,1);Plane $(2x-y+2z+3=0)$

asked Jun 4, 2013 by sreemathi.v

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane (d)Point(-6,0,0),Plane $2x-3y+6z-2=0$

asked May 23, 2013 by rvidyagovindarajan_1

1 answer

Find the $\perp$ distance of the point (2,3,-5) from the plane $x+2y-2z-9=0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Find the $\perp$ distance of the point (3,-2,1) from the plane $2x-y+2z+3=0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angles between them. $(e)\; 4x + 8y + z -8 = 0$ and $y + z -4 =0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither ,then find the angles between them. $(d)\; 2x -y + 3z -1 = 0 \: and\: 2x -y + 3z + 3 = 0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angles between them. $(c)\; 2x -2y + 4z + 5 = 0$ and $3x -3y + 6z - 1 = 0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angle between them. $(b)\; 2x + y + 3z - 2 = 0 \: and\: x -2y + 5 = 0$

asked May 22, 2013 by rvidyagovindarajan_1

1 answer

Find the equations of the planes that passes through three points, $(b)\; (1, 1, 0), (1, 2, 1), (-2, 2, -1)$

asked May 13, 2013 by rvidyagovindarajan_1

1 answer

Find the vector and cartesian equations of the planes $(b) \quad \text{that passes through the point} \; (1, 4, 6) \; \text{and the normal to the plane is } \hat i-2\hat j + \hat k$

asked May 10, 2013 by rvidyagovindarajan_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(d)\;5y + 8 = 0$

asked May 9, 2013 by rvidyagovindarajan_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(c)\; x + y + z = 1$

asked May 9, 2013 by rvidyagovindarajan_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(b)\; 3y + 4z – 6 = 0$

asked May 9, 2013 by rvidyagovindarajan_1

1 answer

Find the Cartesian equation of the following planes: (c) $r .[(s - 2t)\hat i + (3- t) \hat j +(2 s + t) \hat k] = 15$

asked May 8, 2013 by rvidyagovindarajan_1

1 answer

Find the Cartesian equation of the plane $(b)\; \overrightarrow r . (2\hat i +3\hat j - 4\hat k) = 1$

asked May 8, 2013 by rvidyagovindarajan_1

1 answer

In each of the following cases determine the direction cosines of the normal to the plane and the distance from origin(d) $5y+8=0$

asked May 6, 2013 by rvidyagovindarajan_1

1 answer

In each of the following cases determine the direction cosines of the normal to the plane and the distance from origin(c) $2x+3y-z=5$

asked May 6, 2013 by rvidyagovindarajan_1

1 answer

In each of the following cases,determine the direction cosines of the normal to the plane and also the distance from origin(b) $x+y+z=1$

asked May 6, 2013 by rvidyagovindarajan_1

1 answer

Find the angle between the following pair of lines: $\frac{\large x}{\large 2} = \frac{\large y}{\large 2} = \frac{\large z}{\large 1} \: and\: \frac{\large x-5}{\large 4} = \frac{\large y-2}{\large 1} = \frac{\large z - 3}{\large 8}$

asked May 1, 2013 by rvidyagovindarajan_1

1 answer

Find the angle between the pairs of lines: $\overrightarrow r = 3\hat i + \hat j - 2\hat k + \lambda (\hat i - \hat j - 2\hat k)\: and \: \overrightarrow r = 2\hat i - \hat j - 56\hat k + \mu (3\hat i - 5\hat j - 4\hat k)$

asked Apr 30, 2013 by rvidyagovindarajan_1

1 answer

Show that the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\lambda \;and\;\frac{x-4}{5}=\frac{y-1}{2}=z=\mu\;$ intersect. Also,find thier point of intersection.

asked Mar 7, 2013 by sreemathi.v

1 answer

A variable plane is at constant distance p from the origin and meet the axes in A, B & C. Show that the locus of the centroid of the tetrahedron $\bigtriangleup ABC\;is\; \Large\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{16}{p^2}$

asked Feb 5, 2013 by meena.p

1 answer

A variable plane which remains at a constant distance 3p from the origin cuts the co-ordinate axes at A, B & C. Show that the locus of the centroid of the $\bigtriangleup ABC\;is\; \Large\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2}$

asked Feb 5, 2013 by meena.p

1 answer

A line makes angles $\alpha,\beta,\gamma\;and\;\delta$ with the four diagonals of a cube. Prove that $\cos ^2 \alpha+\cos ^2\beta+\cos ^2 \gamma+\cos ^2 \delta=\Large\frac{4}{3}$

asked Feb 5, 2013 by meena.p

0 answers

Find the distance of the point (2,3,4) from the line $\Large\frac{x+3}{3}=\frac{y-2}{6}=\frac{z}{2}$ measured parallel to the plane 3x+2y+2z+5 = 0

asked Feb 5, 2013 by meena.p

0 answers

Find the distance of the point (1,-2,3) from the plane x-y+z = 5 measured parallel to the line $\Large\frac{x+1}{2}=\frac{y+3}{2}=\frac{z+1}{-6}$

asked Feb 5, 2013 by meena.p

0 answers

Find the reflection of the point (1,2,-1) in the plane 3x-5y+4z = 5

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the line passing through the point (3,0,1) and parallel to the planes x+2y = 0 and 3y -z = 0

asked Feb 5, 2013 by meena.p

0 answers

Find the vector equation of the plane through the intersection of the planes $\bar{r}. (2\bar{j}+6\bar{j})+12=0$ & $\bar{r}.(3\bar{i}-\bar{j}+4\bar{k})=0$ which are at a unit distance from the origin.

asked Feb 5, 2013 by meena.p

0 answers

Find the shortest distance between two lines whose vector equations are $\overrightarrow{r}=(1-t)i+(t-2) \bar{j}+(3-2t) \bar{k}$ and $\overrightarrow{r}=(s+1) \bar {i}+(2s-1)\bar {j}-(2s+1) \bar {k}$

asked Feb 5, 2013 by meena.p

0 answers

Find the values of P so that the lines $\Large\frac{1-x}{3}=\frac{7y-14}{2p}=\frac{z-3}{2}$ and $\Large\frac{7-7x}{3p}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles.

asked Feb 5, 2013 by meena.p

1 answer

The foot of the perpendicular drawn from the origin to the plane is (2,5,7). FInd the equation of the plane.

asked Feb 5, 2013 by meena.p

0 answers

Find the perpendicular distance of point (2,3,4) from the line $\Large\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}$

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the plane through the points (-1,1,1) and (1,-1,1) perpendicular to the plane x+2y+2z = 5

asked Feb 5, 2013 by meena.p

1 answer

Find the length and co-ordinates of the foot of perpendicular from point (1,1,2) to the plane 2x-2y+4z+5 = 0

asked Feb 5, 2013 by meena.p

0 answers

Find the foot of the perpendicular drawn from the point A(1,0,3) to the join of the points B(4,7,1) and C(3,5,3)

asked Feb 5, 2013 by meena.p

1 answer

Find the equation of the plane passing through the points (1,-1,2) and (2,-2,2) and perpendicular to the plane 6x-2y+2z = 9.

asked Feb 5, 2013 by meena.p

1 answer

Find the image of the point (1,2,3) in the plane x+2y+4z = 38.

asked Feb 5, 2013 by meena.p

0 answers

Show that the lines $\Large\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\Large\frac{x-4}{5}=\frac{y-1}{2}=2$ intersect. Also find the point of intersection.

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the plane passing through the point (1,1,1) and perpendicular to each of the plane x+2y+3z = 7 and 2x-3y+4z = 0

asked Feb 5, 2013 by meena.p

0 answers

Find the value of k for which the lines $\Large\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\Large \frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are co-planar.

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

Find the value of k for which the two lines $\large\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\; and \;\frac{x-3}{1}=\frac{y-k}{2}=z$ intersect at a point?

asked Feb 5, 2013 by meena.p

0 answers

What are the conditions that the planes $a_1x+b_1y+c_1z=d_1\;and\; a_2x+b_2y+c_2z=d_2$ are (i) parallel (ii) perpendicular to each other?

asked Feb 5, 2013 by meena.p

0 answers

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