Question

given u=(1,3,-2) v=(-2,2,2) w=(5,1,4)

demonstrate that u, v, w are perpendicular to each other.... its a question under cross product and dot product. how should i go about solving it. thanks

Answer 1

you need to dot each vector, or cross 2 to get the third

Answer 2

use the cross product to show that u and v are orthogonal
then v and w
then show that u != w

Answer 3

or, if you row reduce them and they turn to a 1 diagonal, they is good

Answer 4

what is orthogonal?

Answer 5

if:

u.v=0
u.w=0
v.w=0 they is all perped

Answer 6

perpendicular

Answer 7

orthogonal means they are 90 degrees

Answer 8

Its what people say when they want to sound cool while saying perpendicular:P

Answer 9

ok so i should start by finding the cross product of u and v?

Answer 10

yeah, make sure it = 0

Answer 11

id go dot product, its just a simpler method

Answer 12

ok.. after that?

Answer 13

o yeah..dot

Answer 14

u=(1,3,-2)
.v=(-2,2,2)
-----------
-2+6-4 = 0

Answer 15

do that for u.w and v.w to see if they zero out

Answer 16

ok dot product of u and v. gives us 0. whats next?

Answer 17

take out a pencil and paper, and dot the other 2 combinations perhaps?

Answer 18

i.e v and w or u and w

Answer 19

both sets; v and w; AND u and w

you have to determine that they are all perp to each other

Answer 20

i.e all dot product gives us zero.

Answer 21

correct, if one dot product gives us something other than 0, then they aint all perped

Answer 22

gotta pick up the kids, yall have fun

Answer 23

thnks ami..