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.

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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