Find the angle Q between the two vectors.
u = 10i + 40j v = -3j+8k
cos <10,40,0> <0,-3,8> / sqrt1700 sqrt73
cos(-120/sqrt1700 sqrt73) = .9072885394
arc cos (.9072885394) = 24.86 degrees.
Is this correct?
What happened to the - sign in the Cosine term? I think that changes the angle significantly.
I am not sure what to change.
cosine is negative in the second and third quadrant.
To find the angle Q between two vectors, you can use the dot product formula:
u · v = |u| |v| cos(Q)
First, calculate the dot product of the two vectors u and v:
u · v = (10)(0) + (40)(-3) + (0)(8) = -120
Next, calculate the magnitudes of the vectors u and v:
|u| = √(10^2 + 40^2 + 0^2) = √1700
|v| = √(0^2 + (-3)^2 + 8^2) = √(9 + 64) = √73
Now, substitute the values into the formula:
-120 = (√1700)(√73) cos(Q)
Divide both sides by (√1700)(√73):
cos(Q) = -120 / (√1700)(√73)
Simplify further:
cos(Q) = -120 / (√1700 √73) = -120 / (√123100)
Now, to find the angle Q, take the inverse cosine (arc cos) of the resulting value:
Q = cos^(-1)(-120 / (√123100))
Using a calculator, you should get Q ≈ 24.86 degrees.
Therefore, your answer of Q ≈ 24.86 degrees is correct.