Find the angle between u and v in radians.
-u = 8i, v = 6i - 4j
A) 1.56
B) 0.98
C) 0.59
D) 1.14

Question

Quizplus · Accepted Answer

The angle between two vectors can be found using the dot product formula:

cos(theta) = (u dot v) / (magnitude of u * magnitude of v)

where theta is the angle between u and v.

In this case,

u dot v = (8)(6) + (0)(-4) = 48 
magnitude of u = sqrt((8)^2 + (0)^2) = 8 
magnitude of v = sqrt((6)^2 + (-4)^2) = 2sqrt(10)

So,

cos(theta) = 48 / (8 * 2sqrt(10)) = sqrt(15/20) = sqrt(3/4) 
theta = cos^-1(sqrt(3/4)) = 0.59 radians

Therefore, the answer is choice C (0.59).

Find the Angle Between U and V in Radians