Where does the line [x, y, z] = [6, 10, 1] + t[3, 4, -1] meet the xy-plane?

Answer 1

The x-y plane is where z=0.
So solve the equation of the line where z=0, i.e.
z=1+t[-1]=0
=>
t=1
Substitute t=1 into
[x, y, z] = [6, 10, 1] + t[3, 4, -1]
gives
[x,y,z]=[6,10,1]+1[3,4,-1]=[9,14,0]

Answer 2

So the final answer for this one would be
[x,y,z]=[6,10,1]+1[3,4,-1]=[9,14,0] ?

Thank you!

Answer 3

Right.
You're welcome!