If any figure has three dimensions than it has three co-ordinates i.e. X, Y and Z axis. Cartesian Coordinates in Space is denoted by Point ‘P’ which contains three Real Numbers that indicate the positions of the perpendicular projections from the point to three Perpendicular Lines which are called axis. If the Cartesian coordinate contains three points x, y, z then the point ‘x’ is belongs to X axis, point ‘y’ belongs to Y axis and point ‘z’ belongs to Z axis. We can easily write that Cartesian coordinate P = (x, y, z). If we have two, three dimension co-ordinates and we want to calculate the distance between them then we use pythagoras theorem to calculate distance between them. Let’s assume we have two Cartesian coordinates (x1, y1, z1) and (x2, y2, z3) then the distance ‘d’ between two co-ordinates is
=√[ (x2 - x1)2 + (y2 – y1) + (z2 – z1)2]
Now to understand we will take an example of two Cartesian points and find distance between them. We have two Cartesian point A (3, 4, 8) and B (2, 3, 6) then according to formula distance
D = √[(2- 3)2 + (3 – 4 )2 + (6 – 8)2],
After putting the values in the formula we get
D = √[(-1)2 + (-1)2 + (-2)2],
D = √(6) = 2.44.
So the distance between two co-ordinates ‘A’ and ‘B’ is 2.44. If three dimension Cartesian co-ordinates ‘P’ contains three points x = 0, y = 0 and z = 0 then it means that ‘P’ is a point which is situated at the origin O (0, 0, 0) or point ‘P’ and Origin ‘O’ are same and the distance between any point to ‘P’ is same as origin to that point.
Orthogonal projections are defined as the way of representing a three dimensional object into two dimensional representations. It represents parallel form in the projection where all projection lines are obtained as orthogonal and that is to the projection plane. It can be further classified or divided in different types of orthographic projections. First is terme...Read More