Equation of a plane perpendicular to another plane

[Josie Jones]

Hi, I am really stuck! I need to find the equation of the plane through the line x=2y=3z perpendicular to the plan 5x+4y-3z=8. Can anyone give me any pointers of where to start with this? Not expecting a full solution, just an idea of where to start.

THanks!

 

[mfb]

I moved this thread to our homework section. Can you find a line (or just a vector) that is perpendicular to the second plane? What do you know about that line (or vector) relative to one of the planes you are looking for?

 

[Josie Jones]

mfb, thanks for moving the thread.

I don't know how to find a perpendicular line or vector. I think it is a normal vector, but I have not been shown how to do this. I found this question in a book and am unsure how to proceed.

thanks for your reply

 

[Mark44]

Hi, I am really stuck! I need to find the equation of the plane through the line x=2y=3z perpendicular to the plan 5x+4y-3z=8.

I don't know how to find a perpendicular line or vector. I think it is a normal vector, but I have not been shown how to do this. I found this question in a book and am unsure how to proceed.

If the book was a textbook on analytic geometry it should have sections on the equations of lines and planes in space, and how to determine the orientation of these objects.

Given the equation of a plane in standard form, Ax + By + Cz = D, it is very simple to find a normal to the plane. It's also straightforward to find a vector in the direction of a line.

Since you haven't made much of an effort, which is required for homework posts, I am closing this thread. Please go back and do some digging in your book. Another resource is this wikipedia article on planes -- https://en.wikipedia.org/wiki/Plane_(geometry). I'm sure they also have an article on lines in space.