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You are given the vectors
X = (1,1,1), y = (2,1,1) and z = (6,2,2).

(i) Find the Cartesian equation of the plane Π normal to the vector x containing the point (2,1,1).

(ii) Find the parametric equation of the line l through the points (2,1,1) and (6,2,2).

(iii) If l' is given parametrically by l' = x + ty (with x and y defined above), find the point of intersection of l' with the plane Π.

(iv) Find x x y, y x z and [x, y, z].

Give an explanation in geometric terms of what you have found.


Solution Summary

This shows how to find Cartesian and parametric equations, and describe findings geometrically.