Let l be the line that passes through the point P=(239) and is parallel to the line with parametric equation

Question

Let l be the line that passes through the point P=(2,3,9) and is parallel to the line with parametric equations
x= -9+7t
y= 9+5t
z= 8 -9t
The vector equation of l is x=p+td where
p=(___,____,_____)T
d= (___,____,_____)T

Answer 1

All you need to write the equation of a line is a point on the line and the directional vector of the line.

The point on the line is P(2, 3, 9). The directional vector is the same as that of the given line that is parallel to the desired line.

d = <7, 5, -9>

The equation of the line is:

L(t) = P + td = <2, 3, 9> + t<7, 5, -9>