Answer
$r(t) =\lt 2+4t, 2t,-2t \gt ; 0 \leq t \leq 1$
$x=2+4t;\\ y= 2t; \\z=-2t ; \\0 \leq t \leq 1$
Work Step by Step
The General vector line equation for the given two points is defined as:
$r(t)=(1-t) r_0+t \times r_1$
Now, we have $r(t) =(1-t) \lt 2,0,0 \gt +t \lt 6,2,-2 \gt$
$\implies \lt 2,0,0 \gt - \lt 2t, 0 \times t,0 \times t \gt+\lt 6t ,2t, -2t \gt$
$\implies =\lt 2-2t,0,0 \gt +\lt 6t ,2t, -2t \gt$
Hence, we have $r(t) =\lt 2+4t, 2t,-2t \gt ; 0 \leq t \leq 1$
The parametric equations are as follows:
$x=2+4t $ $y= 2t; \\z=-2t$ ;$0 \leq t \leq 1$
