Vectors
posted by samantha .
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.

Vectors 
Steve
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 = BA = (1,3,12)
v = CA = (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
u•v = 11312 = 4 ≠ 0
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