June 11, 2013

The vertices A,B, and C of a triangle are given by the points (−1, 0, 2), (0, 1, 0), and (1,−1, 0), respectively. Find point D so that the figure ABCD forms a plane parallelogram.

Answer:If you have a parallelogram ABCD, then you know the vectors AB and DC need to be equal as they are parallel and have the same length. Since we know that AB=(1,1,2) you can easily calculate D since you (now) know C and CD(=AB). We get for 0D=0C+CD=(1,-1,0)+(1,1,-2)=(2,0,-2) and hence D(2,0,-2).