Consider the points $A(2,1,1),B(-1,-1,10)$ and $C(1,3,-4).$

$($a$).$ Find vectors vec$(AB)$ and vec$(AC).$

$($b$).$ Find the scalar$($dot$)$ product vec$(AB)*vec(AC).$

$($c$).$ Find the angle BAC.

$($d$).$ Find the cross product vec$(AB)$vec$(AC).$

$($e$).$ Find the scalar projection of vector vec$(AB)$ onto vec$(AC).$

$($f$).$ Find the area of the triangle ABC.

$($g$).$ Find the equation of the plane determined by the points $A,B$ and $C.$