Problem:

Determine a vector equation of the line of intersection of the planes and .

Answer(from textbook):

Answers may vary.

Comments:

(Crying)Please help me. The questions involving planes are really frustrating me.(Headbang)

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- June 10th 2008, 08:33 AMMorphayneEquation of the Line of Intersection of two Planes Help
__Problem:__

Determine a vector equation of the line of intersection of the planes and .

Answer(from textbook):

*Answers may vary.*

__Comments:__

(Crying)Please help me. The questions involving planes are really frustrating me.(Headbang) - June 10th 2008, 09:38 AMo_O
Taking the cross product of their normals will give you a vector parallel to the line of intersection, i.e. your direction vector.

Find a position vector that lies on the line of intersection (i.e. that satisfies both equations of the plane). This can be pretty much anything and is why your answer will vary. What you can do is fix a value for x (or y or z) and solve for remaining simpler system of equations for the other 2 variables to get a point common to both planes. This point will form the position vector needed to define your line. - June 10th 2008, 11:45 AMSoroban
Hello, Morphayne!

o_O has the best method.

I'll show you another . . .

Quote:

Determine the equations of the line of intersection of the planes

. . and .

Answer(from textbook):

**Answers may vary.**. . . . . . Finally ... a book that gives fair warning!

. .

We have: .

. . Hence: .

Substitute into [2]: .

We have: .

On the right side, replace with the parameter

And we have: .

Therefore: .

- June 10th 2008, 11:49 AMMorphayne