Final answer:
To find the angle between vectors v and w, we can use the dot product formula: v&w = |v||w|cos(theta). The angle between vectors v and w is approximately 126.06°.
Step-by-step explanation:
To find the angle between vectors v and w, we can use the dot product formula:
v&w = |v||w|cos(theta)
where |v| and |w| are the magnitudes of vectors v and w, and theta is the angle between them.
The dot product of vectors v and w is:
v&w = (2)(3) + (-1)(8) = -2
The magnitudes of vectors v and w are:
|v| = sqrt((2)^2 + (-1)^2) = sqrt(5)
|w| = sqrt((3)^2 + (8)^2) = sqrt(73)
Substituting the values into the formula:
-2 = (sqrt(5))(sqrt(73))cos(theta)
Solving for cos(theta):
cos(theta) = -2/(sqrt(5))(sqrt(73))
Using a calculator to find the inverse cosine of cos(theta), we get:
theta = 126.06°
Therefore, the angle between vectors v and w is approximately 126.06°.