Projection of a line
How to find projection under different conditions
1. If the angle between two lines are known to us
It has been shown in the first diagram. Here, the projection of OA on OB is OM and the projection of OB on OA is ON. In this case, the projections can be
determined by simple trigonometry of right angled triangles. Here, Ѳ is the angle between OA and OB.
Then, from triangle OAM,
Cos Ѳ = OM/ OA
OM = OA Cos Ѳ
Similarly, from triangle OBN,
Cos Ѳ = ON/OB
ON = OB Cos Ѳ
2. If the angle between two lines is not known to us
In order to find the projection of a line on the other line, we have another formula to get the projection when angle between the line is not known to us.
It is shown in second figure. If l, m and n be the direction cosines of the line on which projection is made or on which another line is projected. Now, for the projection of line PQ on
AB ( having direction cosines l, m and n) where P be (x1, y1, z1) and Q be (x2, y2, z2).
Then,
Comments
Post a Comment