Question

Vectors u and v are graphed. Explain in detail each step necessary to find the angle between the two vectors and find the angle in degrees.

V=(-2,-1) and U=(-3,-4)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the angle between two vectors, we can use the formula:

cos(theta) = (u dot v) / (||u|| * ||v||)

where u and v are the given vectors, u dot v is the dot product of u and v, ||u|| is the magnitude of vector u, and ||v|| is the magnitude of vector v.

1. Calculate the dot product of vectors U and V:
U dot V = (-3*(-2)) + (-4*(-1)) = 6 + 4 = 10

2. Calculate the magnitudes of vectors U and V:
||U|| = sqrt((-3)^2 + (-4)^2) = sqrt(9 + 16) = sqrt(25) = 5
||V|| = sqrt((-2)^2 + (-1)^2) = sqrt(4 + 1) = sqrt(5)

3. Substitute the values into the formula:
cos(theta) = 10 / (5 * sqrt(5))

4. Calculate the angle in radians:
theta = arccos(10 / (5 * sqrt(5)))

5. Convert the angle from radians to degrees:
Angle in degrees = theta * (180/pi)

By following these steps, you can find the angle between vectors U and V and determine its value in degrees.