Answer
$(a+b)\times c=a \times c+b \times c$
Work Step by Step
Let $a= a_1i+a_2j+a_3k$; $b=b_1i+b_2j+b_3k$ and $c=c_1i+c_2j+c_3k$
$(a+b)\times c=\begin{vmatrix} i&j&k \\ a_1+b_1&a_2+b_2&a_3+b_3\\c_1&c_2&c_3\end{vmatrix}$
Using property of determinants,we can write
$=\begin{vmatrix} i&j&k \\ a_1&a_2&a_3\\c_1&c_2&c_3\end{vmatrix}+ \begin{vmatrix} i&j&k \\b_1&b_2&b_3\\c_1&c_2&c_3\end{vmatrix}$
$=a \times c+b \times c$
Hence, $(a+b)\times c=a \times c+b \times c$
