Two vectors and have magnitude A = 2.90 and B= 3.00. Their vector product is A X B= -4.91 + 2.08. What is the angle between A and B?
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To find the angle between vectors A and B, you can use the dot product formula:
A · B = |A| |B| cos(θ)
Where A · B is the dot product of A and B, |A| is the magnitude of vector A, |B| is the magnitude of vector B, and θ is the angle between A and B.
In your given problem, A · B = -4.91 + 2.08 = -2.83 (taking the dot product of the given vectors).
Substituting the magnitudes and the dot product into the equation, we have:
-2.83 = 2.90 * 3.00 * cos(θ)
Now, solve for cos(θ):
cos(θ) = -2.83 / (2.90 * 3.00) = -0.3231
To find the angle, we need to take the inverse cosine (arccos) of -0.3231, using a calculator or a math software:
θ = arccos(-0.3231)
Using a calculator, we find:
θ ≈ 110.66 degrees
So, the angle between vectors A and B is approximately 110.66 degrees.