Question

show that

Answer 1

i.j=j.k=k.i=0

Answer 2

\[
\mathbf i = \langle 1,0,0\rangle,
\mathbf j = \langle 0,1,0\rangle,
\mathbf k = \langle 0,0,1\rangle
\]So \[
\mathbf i \cdot \mathbf j = \langle 1,0,0\rangle \cdot \langle 0,1,0\rangle = 0+0+0 =0
\]

Answer 3

Same thing for all other dot products.