Question

Suppose vectors a&b if a x b=c. Show that c is perpendicular to a&b. Please help me.

Answer 1

it is more definitive than this. c is perpendicular to the plane a and b lie in.

you have to start with the definition of cross product
i x j=k
j x k=i
k x i=j

if a= a1 i + a2 j +a3 k and
if b= b1 i + b2 j +b3 k

then you can demonstrate with algebra (do it longhand) that
a x b= the matrix expanded for
i;j;k
a1;a2;a3
b1;b2;b3

if you expand that as a determinant,you get axb

Now notice each component of that determinant (I will do i)
(a2b3-b2a3)i Notice this is i component is the product of the j,k components of the a,b vectors. This component of the cross product is perpendicular to the cross product result.

Answer 2

Thank u so much for your help!