Find the angle between u and v in radians.
-u = 10i - 5j - 9k, v = 4i + 7j - 5k
A) 1.40
B) 1.19
C) 1.57
D) 0.38

Question

Quizplus · Accepted Answer

The angle between u and v can be found using the formula:
cos(theta) = (u dot v) / (||u|| ||v||)
where u dot v is the dot product of u and v, and ||u|| and ||v|| are the magnitudes of u and v, respectively.

Using the given values:
u dot v = (10)(4) + (-5)(7) + (-9)(-5) = 107
||u|| = sqrt((10)^2 + (-5)^2 + (-9)^2) = sqrt(226)
||v|| = sqrt((4)^2 + (7)^2 + (-5)^2) = sqrt(90)

Substituting into the formula, we get:
cos(theta) = 107 / (sqrt(226) * sqrt(90))
=> theta = acos(107 / (sqrt(226) * sqrt(90)))

Using a calculator, we get the value of theta as approximately 1.19 radians. Therefore, the best choice is B with the answer of 1.19.

Find the Angle Between U and V in Radians