Problem $1$:

A plane contains three vectors, $A=\{1,2,-3\},B=\{-2,1,-4\},$ and $C=\{1,-Cy,1\}.$

Determine A $*B$;

Calculate the unit vector $n$ normal to the plane;

Find the value of Cy for which the three vectors are coplanar;

Determine the resultant vector of A$,$ B and C$.$

Problem $2$:

Consider the straight lines AB and AC as shown. Use the cross product to find

the shortest distance $d_1$ from $C$ to the line $AB$;

the shortest distance $d_2$ from $B$ to the line $AC.$