A rectangular box is positioned with its vertices at the following points: A = (0,0,0)C = (2,4,0)E = (0,0,3)G = (2,4,3)
B = (2,0,0)D = (0,4,0)F = (2,0,3)H = (0,4,3)
If the coordinates all have three significant figures,the angle between the line segments AG and AH is closest to:
A) 21.8°.
B) 22.5°.
C) 26.6°.
D) 36.9°.
E) 45.0°.

Question

Quizplus · Accepted Answer

The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them. The dot product of AG and AH is (2)(0) + (4)(4) + (3)(3) = 34. The magnitude of AG is sqrt(2^2 + 4^2 + 3^2) = sqrt(29). The magnitude of AH is sqrt(0^2 + 4^2 + 3^2) = sqrt(25) = 5. Therefore, the cosine of the angle between AG and AH is 34 / (sqrt(29) * 5) = 0.906. The angle between AG and AH is therefore approximately 26.6 degrees.

A Rectangular Box Is Positioned with Its Vertices at the Following