# Vectors

The person who helped me before was not very helpful.

ABC has vertices A(3,2,-5), B(4,-1,7) and C(-8,3,-6).

a) Determine the area of ABC.

b) Determine the coordinates of point D such that ABCD is a parallelogram.

c) Is the parallelogram a rectangle? Justify your answer.

1. Given two vectors u and v, forming two sides of a parallelogram, u+v is the corner opposite (0,0). Here, we can take

u = B-A = (1,-3,12)
v = C-A = (11,1,-1)

The area of ∆ (not ) ABC is half the area of the parallelogram ABCD. So, it is

1/2 |uxv| = 1/2 |(-9,133,34)| = 1/2 √18926 = 68.79

The parallelogram is not a rectangle since

uv = 11-3-12 = -4 ≠ 0

posted by Steve

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