Answer
$5x+2y+z=13$
Work Step by Step
Use equation $$a(x-x_{0})+b(y-y_{0})+c(z-z_{0})=0$$
Already have vector need a point that lies on given line.
Can make any point that lies on the given line simply by plugging in any value for t.
Use t=1:
$(1+1,2-1,4-3(1))$
$(2,1,1)$
Substitute appropriate values:
$5(x-2)+2(y-1)+1(z-1)=0$
$5x+2y+z=13$
