Final answer:
The dot product A . B of vectors A and B in polar notation is approximately -90.064 m^2.
Step-by-step explanation:
The dot product (scalar product) of two vectors in polar notation is given by:
A. B = |A| . |B| . cos(θ)
where:
- |A| and |B| are the magnitudes of vectors A and B,
- θ is the angle between the two vectors.
Given:
- |A| = 8 m,
- |B| = 13 m,
- The angle between the vectors is θ = 312° - 74°.
Calculate the dot product:
A . B = 8 . 13 . cos(312° - 74°)
A . B = 104 . cos(238°)
A . B ≈ 104 . (-0.866)
A . B ≈ -90.064
So, A . B is approximately -90.064 m².