The document discusses three dimensional coordinate systems including rectangular, cylindrical, and spherical systems. It provides formulas for finding the coordinates of an internally or externally divided point on a line between two given points. It also discusses direction cosines of lines, including finding the direction cosine of a line from the origin to a given point. Finally, it discusses plane equations and provides a formula for finding the plane equation that passes through three given points, and how to find the vertical distance from a point to that plane.

1. MAHAMUD HASAN
Three Dimensional(3D)

2. MUTUAL RELATIONSHIP
1.Rectangular System
2.Cylindrical System
3.Spherical System
#Problem:
1.(2,3,0)S.S
2.x^2+y^2+z^2=0C.S

3. SECTION FORMULA
#P(x1,y1,z1) &Q(x2,y2,z2) internally divide m1:m2
x=(m1x2+m2x1)/(m1+m2),
y=(m1y2+m2y1)/(m1+m2),
z=(m1z2+m2z1)/(m1+m2).
#P(x1,y1,z1) &Q(x2,y2,z2) externally divide m1:m2
x=(m1x2-m2x1)/(m1-m2),
y=(m1y2-m2y1)/(m1-m2),
z=(m1z2-m2z1)/(m1-m2).
#Problem: Find the co –ordinates of the point which divides the line
joining two points (2,4,3),(-4,3,7) in the ratio 1:4.

4. DIRECTION COSINE OF A
LINE
#Relationship between direction cosine:
l^2+m^2+n^2=1represents a general equation of direction
cosine of a line.
#Direction cosine of a line joining two points P(x1,y1,z1)
&Q(x2,y2,z2) is:
(x2-x1)/l=(y2-y1)/m=(z2-z1)/n=PQ.
#Problem: Find the direction cosine of the line drawn from
origin to the point
(-6,2,3).

5. PLANE EQUATION
# ax+by+cz+d=0represents a general equation of plane.
#General equation of a plane that passes through a given point
P(x1,y1,z1) is:
a(x-x1)+b(y-y1)+z(z-z1)=0.
#Problem: Find the equation of the plane through the points
(2,3,1),(1,1,3)&(2,2,3).Find also it’s vertical distance from the
point (5,6,7) to this plane.

6. Thank You ForYour Attention