Problem $1$: Flux Normal to a Surface, Adapted from Deen $1-4(15$ PoINTS$)$

Consider a point $P=(x,y,z)=(2\frac{a}{3},\frac{b}{3},2\frac{c}{3}),$ which is on the surface of a spheroid defined by

$(\frac{x}{a}{)}^2+(\frac{y}{b}{)}^2+(\frac{z}{c}{)}^2=1$

Suppose that there is a flux $f$ that has the components

$f=(f_x,f_y,f_z)=(\frac{2a}{3},\frac{b}{3},\frac{2c}{3}).$

$($a$)$ Compute the magnitude of the flux into the spheroid at $P.$

$($b$)$ Compute the magnitude of the flux not into the spheroid at $P.$ In what direction is this portion of $f$

traveling?

Hint: The "Normal and Tangent Vectors" subsection of Appendix A$.8$ will be useful.