Scalar (dot) product: 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. In this case, the dot product of AG and AH is:```AG · AH = |AG||AH|cos(θ) = (2^2 + 4^2 + 3^2)^(1/2) * (0^2 + 4^2 + 3^2)^(1/2) * cos(θ) = 5 * 5 * cos(θ) = 25cos(θ)```Since the coordinates all have three significant figures, the angle between AG and AH can be determined to three significant figures as well. The closest choice to the calculated value of 25cos(θ) is 22.5°.

Scalar (Dot) Product: a Rectangular Box Is Positioned with Its