Question: Find the point of intersection of the line containing the points (3,2,1) and (4,3,3) and the plane containing the points (5,4,2), (3,1,6), and (6,5,3). So confused as how to do this particular one, can anyone help at all especially working out, have tried but getting confused? :o/

First, you need to get the equations of the line and the plane.

The equation of a line is often written in the form:

\vec{l} = \( \begin{array}{c} \\ x\\ y\\ z\end{array}\) + \lambda \( \begin{array}{c} \\ i\\ j\\ k\end{array}\)

And that of a line is:

ax + by + cz = d

Where <x, y, z> is a coordinate of a point on the line, <i, j, k> is the direction vector of the line, <a, b, c> is the normal vector of the plane.

Do you know how to get those?

Question: Find the point of intersection of the line containing the points (3,2,1) and (4,3,3) and the plane containing the points (5,4,2), (3,1,6), and (6,5,3). So confused as how to do this particular one, can anyone help at all especially working out, have tried but getting confused?
Thanks for answer but need further elaboration!

Do not start a new thread for the same question please NeoDarkmatter.

And you didn't reply to my question. Realise that this is not a homework service and that downright explanations and answers are not given like that.

Could you answer my previous question?

-> Do you know how to get those?

Thanks I figured it out, the system wouldn't let me comment yesterday for some reason so had to post again for you to get message and I did say needed help, but is OK now. Also will not let me comment today keeps putting up an applet to log in or join, new to this help desk so can anyone tell me why I cannot make comments?

Okay, don't use the comment system either, it makes it quite confusing to follow. Use the answer box at the very bottom instead :)