Recall some Basic Properties of the Cross Product.

$($i$)$ w $\backslash$times v $=$v $\backslash$times w

$($ii$)$ v $\backslash$times v $=$

$($iii$)$ v $\backslash$times w $=0$ if and only if w $=$v for some scalar $$ or v $=0.$

$($iv$)($v$)\backslash$times w $=$ v $\backslash$times $($w$)=$

$$

v $\backslash$times w

$($v$)($u $+$ v$)\backslash$times w $=($u $\backslash$times w$)+($v $\backslash$times w$)$ and u $\backslash$times $($v $+$ w$)=($u $\backslash$times v$)+($u $\backslash$times w$)$

Use the distributive property $($v$)$ to write the cross product we need to find as a sum of two cross products.

$(4$u $+3$w$)\backslash$times w $=$

$\backslash$times w

$+$

$3$w $\backslash$times