HW$2$: Problem $8$

$(10$ points$)$

Find the vector and parametric equations for the line through the point $P(1,1,1)$ and orthogonal to the plane $-1x-5y+5z=3.$ Vector Form: $$

$1)$

$5)$ Parametric form $($parameter $t,$ and passing through $P$

when $t=0)$:

$x=x(t)=$

$$

$y=y(t)=$

$$

$z=z(t)=$

$$