# Linear Algebra

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So I'm studying for my first exam and I'm stuck on this number.

Given both lines:

D1: (x,y,z) = (2,0,0) + k(0,3,0)
D2: (x,y,z) = (2,0,2) + k(0,0,1)

(a) Give the algebraic equation of the plane containing both lines.

I know that I have to start off by finding the intersection point of both lines, but I can't seem to solve it.

Any help is greatly appreciated!

• Linear Algebra -

The normal to this plane is normal to both lines, so the cross product of the direction vector of these lines will be the normal to the plane.

Finally, find the equations of the plane passing through each of the given points. Both of them should give the same equation, otherwise the planes are parallel.

In the given case, you should end up with a single plane that contains both lines.

• Linear Algebra -

THanks again Mate! You've been a big help lately, I really appreciate it.

• Linear Algebra :) -

You're welcome!

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