Question

Evaluate the expression:
v ⋅ w
Given the vectors:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>

Answer 1

\[v • w = <v_x, v_y, v_z>•<w_x,w_y, w_z> = v_x w_x + v_y w_y + v_z w_z\]

Answer 2

r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
okay so <-3,-8,-3>* <-4,-2,-6>= 3x-4x+-8y8y+-3z-6
?

Answer 3

@IrishBoy123

Answer 4

let's do r • r

r = <8, 8, -6>

r • r = <8, 8, -6>•<8, 8, -6> = <8*8 + 8*8 + (-6)*(-6)> = 64 + 64 + 36 = 164

now, let's do r•v

r•v = <8, 8, -6>•<3, -8, -3> = 8*3 + 8*(-8) + (-6)*(-3) = 24 -64 + 18 = -22

do you get the idea?

r, v & w are vectors. the "dot" product turns vectors into simple (scalar) numbers.

why? what is the point of it all?

well, the idea is incredibly powerful as the dot product is a black box that contains the Law of Cosines without the need for all of the usual kerfuffle -- and it make life incredibly easy in 3-D.

however, you have to be able to process it first. just churn the numbers.

Answer 5

ohh okayyy it makes sense now so -22 would be the answer!?

Answer 6

thank you so much!!!! @IrishBoy123

Answer 7

v = <3, -8, -3>; w = <-4, -2, -6>
v•w = <3, -8, -3>•<-4, -2, -6> = 3(-4) + (-8)(-2) + (-3)(-6) = -12 +16 + 18 = +22

have i confused you, or got the sums wrong. ie, where does the minus sign come into it?

Answer 8

ohh i see so what would i do now! just calculate the last part? -12 +16 + 18 = +22? @IrishBoy123

Answer 9

oh wait nevermind lol the answers 22!

Answer 10

+1

Answer 11

wait what lol

Answer 12

+1 means "well done"

that's all.

Answer 13

oh ahahahaha thanks!! youre a lifesaver @IrishBoy123