Problem $3$: Vector Components $(30\%)$

The outside cellar door is connected to hinges at A and $D$ and is being opened by a force of

magnitude $T_{BC}=70N$ acting at point $B.$

a$)$ Determine the magnitude of the component of $T_{BC}$ parallel to the plane of the door.

b$)$ Determine the magnitude of the component of $T_{BC}$ perpendicular to the plane of the door.

Hint: Use the coordinates of A$,$ B$,$ and D to determine

the direction normal to the door.