If `vec(a).vec(b)=0 and vec(a) xx vec(b)=0, " prove that " vec(a)= vec(0) or vec(b)=vec(0)`.

Explanation

Let `vec(a)*vec(b)=vec(0) and vec(a) xx vec(b) = vec(0) .` Then,
`vec(a) * vec(b) = 0 and vec(a) xx vec(b) = vec(0)`
`rArr(vec(a) = vec(0) or vec(b) = vec(0) or vec(a) bot vec(b)) and (vec(a) = vec(0) or vec(b) = vec(0) or vec(a) || vec(b))`
`rArr vec(a) = vec(0) or vec(b) =vec(0)`

`[:' vec(a) bot vec(b) and vec(a) |\| vec(b) " can never hold simultaneously "].`
Hence, `(vec(a)* vec(b) = 0 and vec(a) xx vec(b) = vec(0) ) rArr( vec(a) = vec(0) or vec(b) = vec(0)).`