Question

Three vector a, b, c are given. Proove that if a┴b, a┴c, b┴c (┴ is symbol for perpendicular) and |a|=|b|=|c|=1 that
a=b x a
b=c x a
c=a x b
(it's vector product)

Answer 1

Hey, I think some problem is there in the first value, the value of a....
It should be symmetrically a= b cross c....
Only then u can get the desired...
And all vectors are following symmetry

Answer 2

@saloniiigupta95 yeah, sorry. It should be:
a=b x c
b=c x a
c=a x b

Answer 3

hmm, would the formula:\[sin~\theta=\frac{u\times v}{|u|~|v|}\]be applicable?

Answer 4

but that's definition of vector product....

Answer 5

@amistre64
do you mean \[\sin \theta = \frac{ |a \times b |}{ |a||b| }\]
? With this formula I could show that the length of cross product is 1. Would that be enough to of a proof that a=b x c ? Perhaps I need to show that (b x c) and a are facing the same side too?

Answer 6

yeah, thats the one i was thinking of :)

Answer 7

sin(t) = sqrt(1-cos^2(t))

cos(t) = u.v/|u||v|

sin(t) = sqrt(1-u.v/|u||v|); but it is given that u and v are parallel; so u.v = 0

sin(t) = 1

was something that i was thinking about