BEvaluate the dot product of the two vectors above. They are separated by an angle of 147° and have magnitudes given by: Vector A: 8.00 Vector B: 10.0
Question
Evaluate the dot product of the two vectors above.
They are separated by an angle of 147° and have magnitudes given by:
- Vector A: 8.00
- Vector B: 10.0
Solution
The dot product of two vectors can be calculated using the formula:
A.B = |A| * |B| * cos(θ)
where:
- A.B is the dot product,
- |A| is the magnitude of vector A,
- |B| is the magnitude of vector B, and
- θ is the angle between the vectors.
Given that |A| = 8.00, |B| = 10.0, and θ = 147°, we can substitute these values into the formula:
A.B = 8.00 * 10.0 * cos(147°)
To find the cosine of 147°, you can use a calculator. The cosine of 147° is approximately -0.891.
So, A.B = 8.00 * 10.0 * -0.891 = -71.28
Therefore, the dot product of the two vectors is -71.28.
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