Chapter 12 - Vectors and the Geometry of Space - Review - Exercises - Page 860: 21

$(1,4,4)$

The parametric equations are: $x=2-t; y=1+3t; z=4t$ $\implies 2x-y+z=2$ $\implies 2(2-t)-(1+3t) +4t=2$ $\implies t=1$ Plug $t=1$ into the parametric equations $x=2-t; y=1+3t; z=4t$ We have: $x=2-1; y=1+3(1); z=4(1)$ This implies that $(x,y,z)=(1,4,4)$