move a point along a plane in 3d space

ave · #1 $Old$ June 22nd, 2009, 12:06 PM

I have a triangle in 3d space, and know all the angles and the coordinates of the 3 corners.
I also have a point on one of the edges
from that point I want to draw a perpendicular line, that follows the plane of the triangle- how would I do this mathematically

Plato · #2 $Old$ June 22nd, 2009, 12:21 PM

Quote:

Originally Posted by ave $View Post$

I have a triangle in 3d space, and know all the angles and the coordinates of the 3 corners. I also have a point on one of the edges from that point I want to draw a perpendicular line, that follows the plane of the triangle- how would I do this mathematically

I not at all sure that I understand what it is you require.

Is this it? Say that $A,~B,~\&~C$ are the three vertices of the triangle and point $D \in \overline {AB}$ .
Now you want a line in the plane of the triangle through $D$ which is perpendicular to $\overline {AB}$ .
If that is the case, the solution a straightforward.

Otherwise, you need to try again to explain the question.

ave · #3 $Old$ June 22nd, 2009, 12:46 PM

Quote:

Originally Posted by Plato $View Post$

I not at all sure that I understand what it is you require.

Is this it? Say that $A,~B,~\&~C$ are the three vertices of the triangle and point $D \in \overline {AB}$ .
Now you want a line in the plane of the triangle through $D$ which is perpendicular to $\overline {AB}$ .
If that is the case, the solution a straightforward.

Otherwise, you need to try again to explain the question.

HI Plato- unfortunately my maths has a few holes when it comes to terminology and symbols, I can understand it quite easily, but have never studied it at uni, this unfortunately is my downfall, so I will try explain what I am looking for in picture form

the red dot will be a point that lies on the edge of a triangle- I need to draw a perpendicular line- (in green) from that point.

if you look in the side view (z/y axis), it must lie on the same plane as the triangle- hope that makes sense??

Plato · #4 $Old$ June 22nd, 2009, 01:27 PM

Then the equation of the line is $\ell (t) = D + t\left[ {\overrightarrow {AB} \times \left( {\overrightarrow {AB} \times \overrightarrow {AC} } \right)} \right]$ .
Where the points are as I said above.
But if you are weak in mathematics that may not help you at all.