Asked 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.
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.
Answers
Answered by
Steve
Given two vectors <b>u</b> and <b>v</b>, forming two sides of a parallelogram, <b>u</b>+<b>v</b> is the corner opposite (0,0). Here, we can take
<b>u</b> = B-A = (1,-3,12)
<b>v</b> = C-A = (11,1,-1)
The area of ∆ (not ) ABC is half the area of the parallelogram ABCD. So, it is
1/2 |<b>u</b>x<b>v</b>| = 1/2 |(-9,133,34)| = 1/2 √18926 = 68.79
The parallelogram is not a rectangle since
<b>u</b>•<b>v</b> = 11-3-12 = -4 ≠ 0
<b>u</b> = B-A = (1,-3,12)
<b>v</b> = C-A = (11,1,-1)
The area of ∆ (not ) ABC is half the area of the parallelogram ABCD. So, it is
1/2 |<b>u</b>x<b>v</b>| = 1/2 |(-9,133,34)| = 1/2 √18926 = 68.79
The parallelogram is not a rectangle since
<b>u</b>•<b>v</b> = 11-3-12 = -4 ≠ 0
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