Recent questions in Three Dimensional Geometry

Coloured balls are distributed in three bags as shown in the table below, a bag is selected at random and then two balls are randomly drawn from the selected bag. They happen to be black and red. what is the probability that they came from bag 1 ?

asked Dec 20, 2012 by thanvigandhi_1

1 answer

In each of the following cases,determine the direction cosines of the normal to the plane and the distance from the origin. $(a)\; z = 2$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector $3\hat i + 5\hat j - 6 \hat k.$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

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

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(a)\; 2x + 3y + 4z -12 = 0$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the vector and cartesian equations of the planes that passes through the point $(1, 0, -2)$ and the normal to the plane is $\hat i+\hat j - \hat k$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the equations of the planes that passes through three points. $(1, 1, -1), (6, 4, -5), (-4, -2, 3)$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the intercepts cut off by the plane $2x + y -z = 5.$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the equation of the plane with intercept 3 on the y - axis and parallel to ZOX plane.

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the equation of the plane through the intersection of the planes $3x -y + 2z -4 = 0$ and $x + y + z -2 = 0$ and the point $(2, 2, 1).$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the vector equation of the plane passing through the intersection of the planes $\overrightarrow r .(2\hat i + 2 \hat j - 3\hat k) = 7, \overrightarrow r .(2\hat i + 5\hat j + 3\hat k ) = 9$ and through the point $(2, 1, 3).$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the equation of the plane through the line of intersection of the planes $x + y + z = 1$ and $2x + 3y + 4z = 5$ which is perpendicular to the plane $x -y + z = 0.$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the angle between the planes whose vector equations are $\overrightarrow r. ( 2\hat i + 2\hat j - 3\hat k ) = 5 \: and\: \overrightarrow r. ( 3\hat i - 3\hat j + 5\hat k ) = 3.$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angles between them. $(a)\; 7x + 5y + 6z + 30 = 0 \: and \: 3x -y -10z + 4 = 0$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane (a)Point(0,0,0),Plane $3x-4y+12z-3=0$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

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

asked Dec 14, 2012 by thanvigandhi_1

1 answer

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

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the shortest distance between the lines whose vector equations are $\overrightarrow r = ( \hat i + 2\hat j + 3\hat k) + \lambda ( \hat i - 3\hat j + 2\hat k )$ and $\overrightarrow r = 4 \hat i + 5\hat j + 6\hat k + \mu (2\hat i + 3\hat j + \hat k )$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the shortest distance between the lines: $\frac{ \large x + 1 }{ \large 7} = \frac{ \large y + 1}{ \large -6} = \frac{ \large z + 1}{ \large 1}$ and $\frac{ \large x - 3 }{ \large 1} = \frac{ \large y - 5}{ \large -2} = \frac{ \large z - 7}{ \large 1}$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the shortest distance between the lines $\overrightarrow r = ( \hat i + 2\hat j + \hat k) + \lambda ( \hat i - \hat j + \hat k )$ and $\overrightarrow r = 2 \hat i - \hat j - \hat k + \mu (2\hat i + \hat j + 2\hat k )$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Show that the lines $\frac{ \large x - 5 }{ \large 7} = \frac{ \large y + 2}{ \large -5} = \frac{ \large z}{ \large 1}$ and $\frac{ \large x }{ \large 1} = \frac{ \large y}{ \large 2} = \frac{ \large z}{ \large 3}$ are perpendicular to each other.

asked Dec 14, 2012 by thanvigandhi_1

1 answer

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

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the line of intersection of the planes $\overrightarrow r. (\hat i + \hat j + \hat k)=1$ and $\overrightarrow r. (2\hat i + 3\hat j - \hat k) + 4 = 0$ and parallel to $x$ - axis.

asked Dec 14, 2012 by thanvigandhi_1

1 answer