Question

BEST RESPONSE
Find a ⋅ b.

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

Answer 1

multiply the two x terms together and multiply the two y terms together. put the results into another ordered pair.

Answer 2

okay can you explain how to do this one?
Find a ⋅ b.

a = 10i + 9j, b = 4i + 3j
is it the same process? @tomo

Answer 3

is this two vectors?

Answer 4

dot products of two vectors yes

Answer 5

@tomo
I don't believe that is correct. If I am right, this is the dot product:
if
x = <a,b> and y = <c,d>,

the dot product is a number!! whose value is
ac + bd

In your case, the dot product is 30.

Answer 6

yes you are correct @khoala4pham

Answer 7

so how would i do
a = 10i + 9j, b = 4i + 3j @khoala4pham

Answer 8

then you have <10,9> <4,3> just follow the same process

Answer 9

okay i have one more quick question!

Answer 10

Evaluate the expression:

v ⋅ w

Given the vectors:

r = <5, -5, -2>; v = <2, -8, -8>; w = <-2, 6, -5>

Answer 11

The same is true for n-dimensional vectors: you take the product of each corresponding coordinate and then take the sum of all of it. Generally,
<a1,a2,a3,a4,...an> (dot) <b1,b2,b3,b4,...bn> =
a1*b1 + a2*b2 + a3*b3 + a4*b4 +...(an)*(bn)

In your case, v (dot) w is
2(-2) + (-8)6 + (-8)(-5) =
-4 - 48 + 40=
-12

Answer 12

Thank you!