Solution
= Solution
The $z$ component of the <cross product> is $2a-2$. For the result to lie in the $x$-$y$ <plane>, it must vanish, giving $a=1$. The <dot product> condition is then $2a+2-3b=0$, so
$$
\boxed{a=1,\qquad b=\frac43}.
$$
= Solution
The $z$ component of the <cross product> is $2a-2$. For the result to lie in the $x$-$y$ <plane>, it must vanish, giving $a=1$. The <dot product> condition is then $2a+2-3b=0$, so
$$
\boxed{a=1,\qquad b=\frac43}.
$$