Question

Find the dot product of vectors uu and vv given that:
u=⟨4,5⟩u=⟨4,5⟩
v=⟨−3,−7⟩v=⟨−3,−7⟩

Answer 1

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.