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The angle θ between the planes A_{1}x + B_{1}y + C_{1}z + D1 = 0 and A_{2 }x + B_{2} y + C_{2} z + D_{2} = 0 is given by
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.
If l, m, n are the direction cosines of a line, then
Find the shortest distance between the lines :
The distance of a point whose position vector is from the plane
Find the angle between the planes whose vector equations are
is a vector joining two points P(x_{1}, y_{1}, z_{1}) and Q(x_{2}, y_{2}, z_{2}). If Direction cosines of are
Find the shortest distance between the lines and
The distance d from a point P(x_{1}, y_{1}, z_{1}) to the plane Ax + By + Cz + D = 0 is
Determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.7x + 5y + 6z + 30 = 0 and 3x – y – 10z + 4 = 0
If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are
Find the angle between the following pairs of lines: and
Determine the direction cosines of the normal to the plane and the distance from the origin. Plane z = 2
In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0
If l, m, n are the direction cosines and a, b, c are the direction ratios of a line then
If a line makes angles 90^{∘}, 135^{∘}, 45^{∘} with the x, y and z – axes respectively, find its direction cosines.
In the vector form, equation of a plane which is at a distance d from the origin, and is the unit vector normal to the plane through the origin is
Determine the direction cosines of the normal to the plane and the distance from the origin. Plane x + y + z = 1
In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0
209 videos443 docs143 tests

NCERT Exemplar: Three Dimensional Geometry Doc  24 pages 
Direction Cosines and Direction Ratios of a Line Doc  4 pages 
Direction Cosines of a Line Doc  16 pages 
Test: Section Formula 3D Geometry Test  10 ques 
Examples: Equation of a Plane Perpendicular to a given Vector and passing through a given point Video  10:48 min 
209 videos443 docs143 tests

NCERT Exemplar: Three Dimensional Geometry Doc  24 pages 
Direction Cosines and Direction Ratios of a Line Doc  4 pages 
Direction Cosines of a Line Doc  16 pages 
Test: Section Formula 3D Geometry Test  10 ques 
Examples: Equation of a Plane Perpendicular to a given Vector and passing through a given point Video  10:48 min 