Use vectors to determine if the points (5, 30, 7), (3, 3, -2), (-6, 0, 9), and (-4, 27, 18) form a square.
A) yes
B) no

Question

Quizplus · Accepted Answer

The vectors between the points are:(5, 30, 7) - (3, 3, -2) = (2, 27, 9)(3, 3, -2) - (-6, 0, 9) = (9, 3, -11)(-6, 0, 9) - (-4, 27, 18) = (-2, -27, -9)(-4, 27, 18) - (5, 30, 7) = (-9, -3, 11)The lengths of these vectors are:|(2, 27, 9)| = sqrt(2^2 + 27^2 + 9^2) = sqrt(810)|(9, 3, -11)| = sqrt(9^2 + 3^2 + (-11)^2) = sqrt(205)|(-2, -27, -9)| = sqrt((-2)^2 + (-27)^2 + (-9)^2) = sqrt(810)|(-9, -3, 11)| = sqrt((-9)^2 + (-3)^2 + 11^2) = sqrt(205)Since the lengths of the vectors are equal, the points form a square.

Use Vectors to Determine If the Points (5, 30, 7)