Question

Find a set of parametric equations for a line that passes through the point <-2,5,4> and is parallel to the xy-plane and yz-plane.

Find a set of parametric equations for a line that passes through the point <-4,5,2> and is perpendicular to the plane given by -x+2y+z = 5

I wanna make sure I'm doing these correctly, not enough examples.

Answer 1

Parallel to xy and yz? So, only y can be altered?

Answer 2

^^ correct
so the line would be:
x(t) = -2
y(t) = t+5
z(t) = 4

part2)
vectors which are perpendicular have dot product of 0
plane vector is coefficients --> <-1,2,1>
line vector is <a,b,c>

-a +2b +c = 0
a = 1
b=1
c = -1

the point (-4,5,2) is initial value when t=0
x(t) = t -4
y(t) = t+5
z(t) = 2 - t