Answer
$x=2+3t,y=4+7t, z=5-5t$
Work Step by Step
The parametric equations of a straight line can be found by knowing the value of a vector, such as $v=v_1i+v_2j+v_3k$, passing through a point $P(x_0,y_0,z_0)$ as follows:
$x=x_0+t v_1,y=y_0+t v_2; z=z_0+t v_3$
Here, we have the vector $v=\lt 3,7,-5 \gt$ perpendicular to the plane with point $P(2,4,5)$ .
Thus, we get the parametric equations:
or, $x=2+3t,y=4+7t, z=5-5t$
