Equation of plane question?

10 points to check my geometry question!!! 1 question!?

• Don't just say "yes" or "no". Give me some feedback if I did it right and how I should have done it if it's wrong. If you just say yes or no you won't get the points. this is the question I had to answer: 1. The equation of a plane in space is x + 3y + 2z = 6. a.) Accurately sketch the plane on the set of axes, showing all your calculations below. b.) The three planes of the axes and the plane you have sketched create a triangular pyramid. Find the volume of this pyramid, showing the formula you are using and all calculations below. ----- My answer: a.) http://i50.tinypic.com/2lsuq6c.png b.) 1/2 x 6 x 2 = 6 is the Area and 1/3 x 6 x 3 = 6 is the Volume I don't think I have A right. :( if i'm wrong correct me. show me how to do it and how it should be.

• Answer:

  a) Divide by 6 (the constant on the right) to put the equation into intercept form: .. x/6 + y/2 + z/3 = 1 This form tells you the axis intercepts, from which we determine that the plane intercepts the x-axis at x=6. You seem to have shown it as x=0. b) You have correctly computed the volume using the x-y plane as the "base" and the distance along the z-axis as the "height" of a pyramid. (Your picture needs to show the triangle you used for the base of the pyramid. It shows only a line.)