Final answer:
The dot product of vectors u=⟨4,5⟩ and v=⟨−3,−7⟩ is found by multiplying corresponding components of the vectors and then summing those products, resulting in a scalar value of -47.
Step-by-step explanation:
Finding the Dot Product of Vectors
The dot product of two vectors is a scalar quantity that results from the multiplication of corresponding components of the two vectors. Given vectors u=⟨4,5⟩ and v=⟨−3,−7⟩, the dot product is calculated as follows:
Dot Product = u1 * v1 + u2 * v2
For our given vectors, that becomes:
Dot Product = (4)(−3) + (5)(−7)
= (−12) + (−35)
= −47
The dot product of vectors u and v is −47. This scalar quantity can have various physical interpretations depending on the context, such as work done by a force or projection of one vector onto another.