What is the Result of i X i in a Cross Product?

[krot]

in the end of this
http://i29.tinypic.com/5fktjo.jpg

i got to the point where it asks what B is
i think that because i X J = K then b should be in the direction of J

but they have a different conclusion
why??

 

[Doc Al]

All you can conclude is that B has a j component.

 

[krot]

its only in j direction
it can't have a component of other vector
because in order to transform i to k
we need pure j

 

[Doc Al]

its only in j direction
it can't have a component of other vector
because in order to transform i to k
we need pure j

No. Let B = ai + bj + ck. When you take the cross product, each term must give a k-component or 0. We know that c must equal 0, since i X k = -j. But what about a?

 

[krot]

one vector is(1,0,0)
the result vector is (0,0,1)
i do this determinant to find the cross product
|i j k |
|1 0 0|
|x y z|
it gives us i*0 +j*z +k*-y or (0,z,-y)
but our result vector is (0,0,1)
so z=0 and y=-1

y=-1 is -j vector

there is no a here
i showed purely by math that the result is pure -j vector

there is no way to have components from other vectors

 

[Doc Al]

i showed purely by math that the result is pure -j vector

No you didn't. What's i X i?