Question

Find the indicated dot product.

r = <9, -7, -8>, v = <3, 4, 7>, w = <6, -9, 7>

v ⋅ w

<-27, 28, 56>
<18, -36, 49>
18
31

Answer 1

At first i thought the formula i needed to use was

\[v*w= (v _{1}*w _{1})+(v _{2}*w _{2})+(v _{3}*w _{3}) \]

But I'm not getting the right answer.. i figure im doing something wrong

Answer 2

that's the cross product

Answer 3

oh.. lol that explains alot

Answer 4

you can use \(\large \overrightarrow u \cdot \overrightarrow v = u_x*v_x+u_y*v_y\)

Answer 5

as usual, wikipedia does it better
"his operation can be defined either algebraically or geometrically. Algebraically, it is the sum of the products of the corresponding entries of the two sequences of numbers."

Answer 6

omg thank you so much !!

Answer 7

just wondering what the answer is, asking for a friend

Answer 8

umm gimme a sec. i had already submitted the exam and got it wrong .. ill do the math though

Answer 9

it's cool if you don't want to, I just wanted to make sure you understood the concept

Answer 10

yeah , no i dont mind.. i still dont understand though.. theres 3 numbers though ? what do i do with the 3rd? the formula only lets me do 2 number

Answer 11

it's the same thing but x,y,z instead of x y

notice the wikipedia articles wording. it says componentwise

there is no formula, that's just the formula for the case where u and v have 2 components

Answer 12

ooohhhhh alright .. gimme a sec again lol

Answer 13

oh, same thing for 3 vectors btw

Answer 14

\[v = \langle v_0, v_1, v_2\rangle,\quad w = \langle w_0, w_1, w_2\rangle \]
\[v\cdot w=\langle v_0, v_1, v_2\rangle\cdot \langle w_0, w_1, w_2\rangle\\
\qquad=v_0w_0+v_1w_1+v_2w_2\]

Answer 15

i got 31

Answer 16

so \(u*v*w = u_x v_x w_x + u_y v_yw_y+u_zv_zw_z\)

Answer 17

the dot product of two vectors, is simply the sum of the products of the corresponding componets

Answer 18

\[\checkmark\]

Answer 19

Thank you both of you ! Big help !