How does this math problem work?

(a)

The plane through P normal to the direction vector of the straight line:

-x+y+z=-4+6-2=0

So: E: x-y-z=0

Now determine the intersection S of the straight line with the plane E.

The length of the distance SP is the desired distance.

(b)

you can return to the calculation of the distance between the two levels E1 and E2

place E1 and E2 in each case in parameter form.

E1 has the support point of g and the direction vectors of g and h

E2 has the support point of h and the direction vectors of g and h