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Coordinate Geometry

Angle in 3D space

- Angle between line and plane given coefficients of line and plane
- Angle between two lines given direction cosines of that two lines w.r.to x, y & z axis
- angle between two lines given direction ratios of that two lines w.r.to x, y & z axis
- Angle between two planes
- Angle made by direction cosines of two lines in sine form

Coefficients in 3D Space

- Constant coefficient of plane 2 given distance between 2 || planes & direction ratios of planes
- Constant coefficient of plane given ⊥ distance between plane and a point and coordinates of point
- Constant coefficient of sphere given centre & radius of sphere of form x2+y2+z2+2ux +2vy+2wz+d=0
- D in std. equation of plane using dist. b/w 2 || planes,D.R.s given distance is positive
- Ratio in which line joining two points P & Q is divided by plane xy
- Ratio in which line joining two points P & Q is divided by plane yz
- Ratio in which line joining two points P & Q is divided by plane zx

Direction cosine in 3D Space

- Direction cosine of a line w.r.to x-axis
- Direction cosine of a line w.r.to y axis
- Direction cosine of a line w.r.to z axis
- Direction cosine of line1 w.r.to x axis given angle between line 1 & 2
- Direction cosine of line1 w.r.to y axis given angle between line 1 & 2
- Direction cosine of line1 w.r.to z axis given angle between line 1 & 2
- Direction cosine of line2 w.r.to x axis given angle between line 1 & 2
- Direction cosine of line2 w.r.to y axis given angle between line 1 & 2
- Direction cosine of line2 w.r.to z axis given angle between line 1 & 2
- Direction cosine of plane1 w.r.to x axis given plane1 & 2 are || & direction cosines w.r.to y axis
- Direction cosine of plane1 w.r.to x axis given plane1 & 2 are || & direction cosines w.r.to z axis
- 22 More formulas!

Direction ratio

- Direction ratio given projection of line on x axis and length of line
- Direction ratio given projection of line on y axis and length of line
- Direction ratio given projection of line on z axis and length of line
- Direction ratio of a line given x coordinates of end points of line
- Direction ratio of a line given y coordinates of end points of line
- Direction ratio of a line given z coordinates of end points of line
- Direction ratio of plane w.r.to x axis given ⊥ distance between plane and a point
- Direction ratio of plane w.r.to y axis given ⊥ distance between plane and a point
- Direction ratio of plane w.r.to z axis given ⊥ distance between plane and a point
- Direction ratio w.r.to x axis given distance between 2 || planes & constant coefficients
- Direction ratio w.r.to y axis given distance between 2 || planes & constant coefficients
- 2 More formulas!

Distance in 3D space

- ⊥ distance from the origin to the plane given direction cosine w.r.to x axis
- ⊥ distance from the origin to the plane given direction cosine w.r.to y axis
- ⊥ distance from the origin to the plane given direction cosine w.r.to z axis
- ⊥ distance from the origin to the plane given direction cosines of normal from origin to plane
- D in std equation of a plane given dist. b/w || planes,D.R.s taking dist. -ve
- Distance between 2 || planes of form ax + by + cz + d1 = 0 & ax + by + cz + d2 = 0
- Distance between 2 points in 3D space
- Distance between plane in normal formal and a point
- Distance between two points P(x1,y1,z1) & Q(x2,y2,z2)
- Distance of a point from origin
- Distance of a point from plane
- 17 More formulas!

x coordinates in 3D space

- x coordinate of a point given distance from origin to point and y & z coordinate of that point
- x coordinate of a point given y coordinate and Perpendicular distance of that point from z axis
- x coordinate of a point given z coordinate and Perpendicular distance of that point from y axis
- x coordinate of centre of sphere given radius and y, z coordinates of sphere
- x coordinate of centre of sphere of form x2+y2+z2+2ux +2vy+2wz+d=0 & radius of sphere
- x coordinate of centre of sphere of form x2+y2+z2+(2u/a)x+(2v/a)y+(2w/a)z+ d/a=0
- x coordinate of centroid of tetrahedron
- x coordinate of centroid of triangle
- x coordinate of foot of perpendicular N from the origin on the plane
- x coordinate of normal given direction cosines & ⊥ distance from the origin to the plane
- x coordinate of point dividing the line joining P & Q at middle
- 8 More formulas!

y coordinates in 3D space

- y coordinate of a point given distance from origin to point and x & z coordinate of that point
- y coordinate of a point given x coordinate and Perpendicular distance of that point from z axis
- y coordinate of a point given z coordinate and Perpendicular distance of that point from x axis
- y coordinate of centre of sphere given radius and x, z coordinates of sphere
- y coordinate of centre of sphere of form x2+y2+z2+2ux +2vy+2wz+d=0 & radius of sphere
- y coordinate of centre of sphere of form x2+y2+z2+(2u/a)x+(2v/a)y+(2w/a)z+ d/a=0
- y coordinate of centroid of tetrahedron
- y coordinate of centroid of triangle
- y coordinate of foot of perpendicular N from the origin on the plane
- y coordinate of normal given direction cosines & ⊥ distance from the origin to the plane
- y coordinate of point dividing the line joining P & Q at middle
- 8 More formulas!

z coordinates in 3D space

- z coordinate of a point given distance from origin to point and x & y coordinate of that point
- z coordinate of a point given x coordinate and Perpendicular distance of that point from y axis
- z coordinate of a point given y coordinate and Perpendicular distance of that point from x axis
- z coordinate of centre of sphere given radius and x, y coordinates of sphere
- z coordinate of centre of sphere of form x2+y2+z2+2ux +2vy+2wz+d=0 & radius of sphere
- z coordinate of centre of sphere of form x2+y2+z2+(2u/a)x+(2v/a)y+(2w/a)z+ d/a=0
- z coordinate of centroid of tetrahedron
- z coordinate of centroid of triangle
- z coordinate of foot of perpendicular N from the origin on the plane
- z coordinate of normal given direction cosines & ⊥ distance from the origin to the plane
- z coordinate of point dividing the line joining P & Q at middle
- 8 More formulas!

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