Use vectors to determine if the points (3, -1, 0), (3, -3, -1), (0, 1, -9), and (0, 3, -8) form a square.
A) yes
B) no

Question

Quizplus · Accepted Answer

The vectors between the points are:(3, -3, -1) - (3, -1, 0) = (0, -2, -1)(0, 1, -9) - (3, -1, 0) = (-3, 2, -9)(0, 3, -8) - (0, 1, -9) = (0, 2, 1)(3, -1, 0) - (0, 3, -8) = (3, -4, 8)The lengths of these vectors are:|0, -2, -1| = sqrt(0^2 + (-2)^2 + (-1)^2) = sqrt(5)|-3, 2, -9| = sqrt((-3)^2 + 2^2 + (-9)^2) = sqrt(90)|0, 2, 1| = sqrt(0^2 + 2^2 + 1^2) = sqrt(5)|3, -4, 8| = sqrt(3^2 + (-4)^2 + 8^2) = sqrt(90)Since the lengths of the vectors are all equal, the points form a square.

Use Vectors to Determine If the Points (3, -1, 0)