Final answer:
The dot product of vectors u and v with magnitudes ||u||=45, ||v||=30 and an angle of 5π/6 between them is -2025√3/2.
Step-by-step explanation:
To find the dot product (u · v) using the alternative form of the dot product, we can use the formula that relates the magnitudes of two vectors and the angle between them. The formula for the dot product in terms of magnitudes of vectors and the angle between them is u · v = ||u|| ||v|| cos(θ), where ||u|| is the magnitude of vector u, ||v|| is the magnitude of vector v, and θ is the angle between the vectors. Given that ||u||=45, ||v||=30 and the angle between u and v is 5π/6, we can plug these values into the formula to calculate the dot product:
u · v = 45 × 30 × cos(5π/6).
Since cos(5π/6) is equal to -√3/2, we have:
u · v = 45 × 30 × (-√3/2) = -2025√3/2.
Therefore, the dot product of vectors u and v is -2025√3/2.