Final answer:
To find the angle between vectors v and w, we can use the dot product formula. The angle between v and w is approximately 62.62 degrees, which is closest to 60 degrees.
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(θ)
First, we need to find the magnitudes of v and w. The magnitude of vector v is:
|v| = sqrt((5)^2 + (4)^2) = sqrt(25 + 16) = sqrt(41)
Similarly, the magnitude of vector w is:
|w| = sqrt((6)^2 + (-1)^2) = sqrt(36 + 1) = sqrt(37)
Now, substitute the values into the dot product formula:
v · w = (5)(6) + (4)(-1) = 30 - 4 = 26
Using the dot product value, we can solve for the angle (θ) using the formula:
cos(θ) = (v · w) / (|v| |w|)
cos(θ) = 26 / (sqrt(41) sqrt(37))
Using a calculator to find the cos(θ) value, we get approximately 0.4664. To find the angle, we can use the inverse cosine function:
θ = cos-1(0.4664) ≈ 62.62°
Therefore, the angle between vectors v and w is approximately 62.62°. The closest option to this angle is 60°, so the answer is b) 60 degrees.