Question

Evaluate the expression.

r = <5, 9, -4>, v = <3, 3, -8>, w = <9, -6, -1>

v ⋅ w

Answer 1

what have you tried? where are you stuck?

Answer 2

When I try to subrtact them I just don't get the right answer

Answer 3

this is a dot product of two vectors. Do you know how to calculate the dot product?

Answer 4

no

Answer 5

if you have two vectors: \(a=<a_x,a_y,a_z>\) and \(b=<b_x,b_y,b_z>\), then their dot product is defined as:\[a.b=a_xb_x+a_yb_y+a_zb_z\]

Answer 6

So then I'm just trying to multiply each of them together?

Answer 7

multiply each component of the vectors and add the result - yes.

you may find this site helpful to learn more about this: https://www.mathsisfun.com/algebra/vectors-dot-product.html

Answer 8

Ok thank you, I thought that I was trying to subtract the two..

Answer 9

yw :)

Answer 10

I have another question..

Answer 11

<--- please post each question separately on the left

Answer 12

It is about this

Answer 13

oh - sorry - then go ahead please

Answer 14

No problem.. what happens when you have a variable in the dot product?

Answer 15

a = 6i - 6j, b = 4i + 2j

like if it where something like this

Answer 16

Would you follow the same operations?

Answer 17

the above is equivalent to saying that you have these two vectors:\[a=<6,-6>\]\[b=<4,2>\]The 'i' and 'j' represent the two orthogonal components of each vector.

Answer 18

Ohh, Ok! Thanks Again!

Answer 19

e.g. in you question, \( = <3, 3, -8>\) is equivalent to writing:\[v=3i+3j-8k\]

Answer 20

Ok, are you required to write in that form at all or is it just a teacher thing?

Answer 21

both forms are valid - use whatever method your teacher has taught you but being aware of both will help you understand vectors better

Answer 22

Thanks Again!

Answer 23

yw :)