Ok, let's break this down.
For a vector équation of a straight line, we want to be able to start at any point which we know is on the line, and then follow the direction of the line to be able to get to any other point. That's the whole point of having an equation for it.
Now, the direction of the line, you are told, is perpendicular (at a right angle to) to the x-y plane. So if you imagine the x-y plane drawn on a piece of paper, the line is actually coming straight up out of the paper. Can you express this direction as a vector?
Now, the idea is to write the vector equation of the line (call it L) as
L=a+λbWhere
a is a point you know about, and
b is the direction vector. We've multiplied this direction vector by the constant
λ (which can be anything). So the idea is that you start at
a, then choose how far you want to go in the direction that the line is going in. That choice is
λHope this helps.