Question

[vectors] How are a x b (a cross b) and b x a (b cross a) related?

Answer 1

one goes up, the other goes down

Answer 2

\[\vec a x\vec b = \vec v\]
\[\vec b x\vec a = -\vec v\]

Answer 3

how would i write an expresson to relate them?

Answer 4

id try using symbols and notations that are reminiscent of the course you are taking tho

Answer 5

that looks similar. but would that relate the two? is that what shes asking for?

Answer 6

and will it work for any pair of verctors?

Answer 7

i dont think its asking for proof perse; just trying to see if you recognize that the cross product is not commutative

Answer 8

yeah i was taught that it was not.

Answer 9

yes it will work for any pair of vectors ... within specifications of course:

for example: <1,2> x <2,2,5> is undefined unless we allow the V^2 to be within the V^3

Answer 10

<1,0,0> x <0,1,0> = <0,0,1>

but

<0,1,0> x <1,0,0> = <0,0,-1>

Answer 11

how would i do it for 3 vectors? (assuming that they are given)

Answer 12

ex. a cross (b+c)

Answer 13

b+c is just another vector: say v; therefore a x v

Answer 14

i think the cross is distributive

Answer 15

axb + axc but i cant recall the properties too clearly

Answer 16

so if i was given a= (2,4,6) b=(-1,2,-5) c=(4,3,-1) how do i sub them into the b+c? i only know how to do the tow cross

Answer 17

you know how to cross but not add vectors?

Answer 18

yeha i know how to add vectors so i would add then firs and then corss?

Answer 19

yes; but compare that to the distribution of the cross and see if you get the same results

Answer 20

if: ax(b+c) = axb + axc then my hunch is right :)

Answer 21

ok thanks alot!