Recent questions tagged ch11

Find the vector equation of the line which is parallel to the vector $3\hat i+2\hat j+6\hat k$ and which passes through the point $(1,-2,3).$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the position vector of a point A in space such that $\overrightarrow{OA}$ is inclined at $60^{\circ}$ to OX and at $45^{\circ}$ to OY and $\mid \overrightarrow{OA}\mid$=10 units.

asked Jan 3, 2013 by sreemathi.v

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