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I have been working on these two problems for a while now and I can't seem to come up with the right procedure to take them on:

1) Find the plane through the origin and parallel to the plane 2x - y + 3z = 1

* I thought this could be solved by taking the vector of the parallel plane <2, -1, 3> and cross multiplying with the origin, but that didn't get me anywhere.

2) Find the plane that passes through (1, 2, 3) and contains the line x=3t, y=1+t, z=2-t

* The same problem occurred in this case.

I know how to find a plane when given a point and a normal (perpendicular) vector... what would be of great help is if anyone could help me understand how to find the equation of planes under different circumstances (like the two problems above). Thanks a bunch =)

1) Find the plane through the origin and parallel to the plane 2x - y + 3z = 1

* I thought this could be solved by taking the vector of the parallel plane <2, -1, 3> and cross multiplying with the origin, but that didn't get me anywhere.

2) Find the plane that passes through (1, 2, 3) and contains the line x=3t, y=1+t, z=2-t

* The same problem occurred in this case.

I know how to find a plane when given a point and a normal (perpendicular) vector... what would be of great help is if anyone could help me understand how to find the equation of planes under different circumstances (like the two problems above). Thanks a bunch =)

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