Homework Help: Vectors 2

1. Feb 26, 2010

icystrike

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Last edited: Feb 26, 2010
2. Feb 27, 2010

gabbagabbahey

It's not clear to me what your method is here, but your result doesn't seem correct.

Your result contains the point (3,0,1) and also (just picking a random point in the plane) (1,2,1); and therefor the vector (3,0,1)-(1,2,1)=(2,-2,0) is parallel to your plane.

Now, the plane $\Pi_1$ contains the points (1,-1,7) and (0,-7,0), so the vector (1,-1,7)-(0,-7,0)=(1,6,7) is parallel to $\Pi_1$.

If your plane were really perpendicular to $\Pi_1$, then any vector parallel to your plane would be perpendicular to any vector parallel to $\Pi_1$ and hence you would expect $(2,-2,0)\cdot(1,6,7)$ to be zero; but it clearly isn't.

If you explain your reasoning for each step, and state your reults for parts (i) through (iii), I may be able to see where you are going wrong. A jumbled mess of equations, without any explanation is not a solution.