Find the angle between the vectors u and v if
u = (-1,4)
v = (3,-4)
a. 155.93
b. 158.58
c. 158.13
d. 155.24
e. 157.17
just plug in your numbers:
cosθ =
u•v
-----------------------
|u| |u|
I've tried this and got - 0.9216353751380653
can you help me any further please?
To find the angle between two vectors, u and v, you can use the dot product formula:
u · v = |u| |v| cos(theta)
Where u · v is the dot product of u and v, |u| and |v| are the magnitudes of vectors u and v, and theta is the angle between the two vectors.
Step 1: Calculate the dot product of u and v:
u · v = (-1)(3) + (4)(-4) = -3 - 16 = -19
Step 2: Calculate the magnitudes of u and v:
|u| = √((-1)^2 + 4^2) = √(1 + 16) = √17
|v| = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5
Step 3: Substitute the values into the equation to solve for cos(theta):
-19 = (√17)(5)cos(theta)
Step 4: Solve for cos(theta):
cos(theta) = -19 / (√17 * 5) = -19 / (5√17)
Step 5: Use the inverse cosine function to find the angle:
theta = arccos(-19 / (5√17))
Using a calculator, you should find that theta ≈ 155.93 degrees.
Therefore, the correct answer is (a) 155.93.