Parallel planes and intersecting planes
Hey! I am having trouble with a question, and I am hoping one of you can help me with it!
For what values of k will the planes 2x - 6y + 4z + 3 = 0 and 3x - 9y + 6z + k = 0
i) not intersect?
ii) intersect in a line?
iii) intersect in a plane?
i) for them to not intersect the planes must be parallel. If I multiply plane (1) by 1.5 I get the values in plane (2). Therefore if I set the k value to something that s not a scalar quality of the C value in (1) the planes will be parallel. So:
3x - 9y + 6z + 4 = 0
ii) I believe these two planes to be parallel, so by this logic these two planes can never meet. Therefore no k value will make these planes intersect in a line.
*Unsure about this
iii) I don't understand what the question means by "intersect in a plane". If it means all values of the planes are the same, then I would set the k value to a scalar value of k in the first question. So:
1.5x3 = 4.5
3x - 9y + 6z + 4.5 = 0
I have no idea if I am correct in my thinking here or not. I hope someone here can help me in these solutions!