Question

Find a ⋅ b.

a = <5, 2>, b = <4, 5>

Answer 1

a ⋅ b is referring to the dot product

Answer 2

so if a = <p,q> and b = <r,s>

where p,q,r,s are scalars, then

a ⋅ b = p*r + q*s

Answer 3

In this case,

a = <p,q>
a = <5,2>
so p = 5, q = 2

b = <r,s>
b = <4, 5>
so r = 4, s = 5


which means

a ⋅ b = p*r + q*s

a ⋅ b = 5*4 + 2*5

a ⋅ b = 20 + 10

a ⋅ b = 30

Answer 4

Thank you!

Answer 5

you're welcome

Answer 6

so basically just mulitiply them and then add

Answer 7

yes, the corresponding coordinates, then add the products