Calculate the angle between a and b (correct to the nearest degree).
E) None of these

Question

Calculate the angle between a and b (correct to the nearest degree). 
E) None of these

Quizplus · Accepted Answer

Use the dot product formula: a*b = |a|*|b|*cos(theta)
where |a| and |b| are the magnitudes of vectors a and b respectively, and theta is the angle between them. We have a = (4, -3, 5) and b = (-2, 6, 1). 
|a| = sqrt(4^2 + (-3)^2 + 5^2) = sqrt(50), 
|b| = sqrt((-2)^2 + 6^2 + 1^2) = sqrt(41).
a*b = (4*-2) + (-3*6) + (5*1) = -8 -18 + 5 = -21
Therefore, -21 = sqrt(50)*sqrt(41)*cos(theta)
cos(theta) = -21/(sqrt(50)*sqrt(41)) ≈ -0.850
Taking the inverse cosine, we get theta ≈ 146 degrees.
Rounded to the nearest degree, the answer is 146 degrees, which corresponds to choice C).

Calculate the Angle Between a and B (Correct to the Nearest