Question

Let v = (1,-3) and w = (-2,6). Which of the following is true?

***choose ALL that apply!!****

A. v x w = 36

B. The x-component of v is -2.

C. The y-component of w is 6.

D. w = -2v

**not sure how to do this :( @terenzreignz how do you solve this? :D

Answer 1

@terenzreignz :)

Answer 2

C

Answer 3

uh-oh a cross product... uhhh

Answer 4

but how did you get that? :/

and also it's choose ALL that apply... i don't get how to get to the solution though :(

ooh! yay :) ur here :)

Answer 5

Which ones have you checked?

Answer 6

idk how to check them really :(

like for A, when it says v x w=36.. how do i multiply (1,-3) and (-2,6) ?? is it like FOIL kinda?:/

Answer 7

ehh, not exactly... cross product.... by any chance, do you know how to get determinants of matrices?

Answer 8

errr not really :( how do u do that?

Answer 9

well, at least i don't think i know it haha :P

Answer 10

okay, then...

Answer 11

Let's just use a formula for cross products?

Answer 12

kk :)

Answer 13

<a , b , c> x <p , q , r>
=

<br - qc , cp - ra , aq - pb>

If this formula looks monstrous, that's because it is :D
However, you might want to try u x v now...

Answer 14

sorry, I mean v x w

Answer 15

kk... :/ yeah it looks monstrous haha :/

how do i plug that in? :/

Answer 16

well, <a,b,c> are the components of v
while <p,q,r> are the components of w.

Answer 17

v = (1,-3) and w = (-2,6)

so do multiply them in a FOIL-like method? :/

Answer 18

Wait a minute... I'm such a...

Answer 19

*do i

Answer 20

Sorry, (a) is clearly not true... cross product is ONLY DEFINED for 3-dimensional vectors...

Answer 21

okay i see :) so its narrowed down to B,C, and D! :)

Answer 22

Well, as for B...

Answer 23

but idk how to see if any of B,C, or D are true :/

Answer 24

what IS the x-component of v?

Answer 25

1?

Answer 26

Yup.... definitely not -2

Answer 27

ohh so B is FALSE right? cuz -2 is the x component for w!

Answer 28

okay, so C is an answer right? cuz y for w= 6.. is that right? :D

Answer 29

strictly speaking, simply because -2 is NOT the x-component of v :D

Answer 30

haha :) yup!!

Answer 31

C... check it :D

Answer 32

yay! kk :) what about D tho? :/

Answer 33

What about C?

Answer 34

oh haha oops i said that above lol :P


okay, so C is an answer right? cuz the y component for w= 6.. is that right? :D

Answer 35

yes... now check D...

Answer 36

-2(1,-3) = -2, 6 which is the same as w!! so C and D are the answers then!? :)

Answer 37

Yes. Very good :D

Answer 38

awesome! thank you so much! :D

Answer 39

awesome! thank you so much! :D