Thread: vector calc

prove that b x a = -a x b

i know how to do it if i make like an example with numbers but how can i show this otherwise? anyone want to start off the proof for me, i'm just kind of stuck

you've got the right idea

just start with a = a1i +a2j +a3k and b = b1 i + b2j +b3k

and then just brute force and ignorance

also it is obvious from the right hand rule but I don't think you want
to hand in pictures of your hands

so i started with
b x a= (a3*b2-a2*b3, a1*b3-a3*b1, a2*b1-a1*b2)
a x b= (a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1)

how should i show that b x a= -a x b
should i just put numbers into what i have above?

Nice work

to finish you could say by inspection a x b = -b x a

or - a x b = -(a2*b3-a3*b2, a3*b1-a1*b3, a1*b2-a2*b1)

= (a3*b2-a2*b3, a1*b3-a3*b1, a2*b1-a1*b2)

= b x a

thank you very much
sorry for bugging you i just have one more question i promise
i am finding the area of the triangle with vertices (0,6,0) (-5,7,1) and (2,1,2)

i got a= (5,-1,-1) and b= (7,-6,1)
and i think the formula is A= 1/2 ll a x b ll
so then i did the square root of the determinates squared and got the square root of (-5)^2 + (-2)^2 + (37)^2 which is definitely not right

the answer is 19/sqrt of 2...

A couple of small mistakes computing a x b

a x b = -7 i -12 j -23 k

See attachment--signs are always a pain in the ass when doing determinants

oh man i made some dumb mistakes haha i think i just couldn't see them because i was getting so frustrated and tired of doing my homework. thanks so much!

The imprtant thing is you have the right skills

1. you knew you needed 1/2(axb)

2.you knew how obtain the vectors a and b

these are very encouraging signs