Find the angle between u and v in radians.
-u = -9i + 10j - 4k, v = 2i + 10j - 5k
A) 0.69
B) 1.57
C) 1.25
D) 0.88

Question

Quizplus · Accepted Answer

We use the dot product formula to find the angle between u and v:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of u and v, respectively, and θ is the angle between them.

First, we need to find |u| and |v|:

|u| = sqrt((-9)^2 + 10^2 + (-4)^2) = sqrt(221)
|v| = sqrt(2^2 + 10^2 + (-5)^2) = sqrt(129)

Next, we need to find the dot product:

u · v = (-9)(2) + (10)(10) + (-4)(-5) = 11

Now we can solve for θ:

11 = sqrt(221) sqrt(129) cosθ

cosθ = 11 / (sqrt(221) sqrt(129))

θ = cos^-1(11 / (sqrt(221) sqrt(129)))

θ ≈ 0.88 radians, which corresponds to answer choice D.

Find the Angle Between U and V in Radians