Question

Give the following three vectors u=2i-j+k, v=i+j+2k, w=2i-j+4k. Determine the scalars such that w-gu-hv is perpendicular to both u and v.

Answer 1

determine scalars g and h such that .... = uxv

Answer 2

^better than my explanation :D

Answer 3

i was hoping your explanation would fill in some of the details :)

Answer 4

could you eloborate :)

Answer 5

i just need something to get me started

Answer 6

keep g and h generac as you combine the vectors; and then equate it to uxv to solve for the scalars

Answer 7

\[\vec w-g\vec u-h\vec v=...\]write out the expression for the components and call the resulting vector r
we know that two vectors are perpendicular if their dot product is zero\[\vec r\cdot\vec u=\vec r\cdot\vec v=0\]solve for the scalars

Answer 8

hmm, okay thanks i get what you mean

Answer 9

are you learning about Gram-Schmidt?

Answer 10

find the projection, and subtract it off is the basic idea.

Answer 11

oh no, just calc 3 chap on cross product.

Answer 12

i will good Gram-Shmidt, sure seems easier

Answer 13

google*

Answer 14

-gu=<-2g,1g,-1g>, -hv=<-1h,-1h,-2h>, w=<2,-1,4>



w=< 2 ,-1 , 4 >
-gu=<-2g,1g,-1g>
-hv=<-1h,-1h,-2h>
-------------------
<2-2g-h, g-h-1, 4-g-2h> = uxv

Answer 15

uxv:

x 2 1 x=-2-1
y -1 1 -y=(4-1)
z 1 2 z = 2+1

uxv = <-3,-3,3>

Answer 16

yes, but they expect you to use the cross product, see amistre

Answer 17

compare parts :)

-3 = 2-2g-h
-5 = -2g-h
h = 5-2g ; see below, since g=1, h=3

-3 = g-h-1
-3 = g-(5-2g)-1
-2 = g-5+2g
3 = 3g; g=1

lets see if this makes the final result work out, crosses fingers

3 = 4-g-2h
3 = 4 -1-2(3)
3 = 4-1-6

3=-3 hmmm

its close so im sure its a typo in there someplace

Answer 18

very cool, thanks now let me go ahead and try it myself,so i can be ready for this exam i got next week

Answer 19

you'll get it.

Answer 20

the concepts good i believe so just keep an eye on the mathing lol