Using components show that vector u cross vector v = the 0 vector if u and v are collinear.
What does the fact that u and v are colinear tell us?
if two vectors are colinear then the vectors are scalar multiples of each other
let$\displaystyle u =(a,b,c)$ and $\displaystyle v= t\cdot u =(ta,tb,tc), t\ne 0$
Then
$\displaystyle u \times v = \begin{vmatrix}
i && j && k \\
a && b && c \\
ta && tb && tc \\
\end{vmatrix}= (b(tc)-c(tb)) \vec i - (a(tc)-c(tc)) \vec j +(a(tb)-b(ta)) \vec j= \vec 0$