Direction vector of a line

Question

Information given: The line $x = 0 , z = \frac{1}{\sqrt{2}}$.

What I need to find: The direction vector.

Where I'm at: I just don't really understand how to get a direction vector from two equation.

The answer to this problem: Vector $\vec{j}$

Answer 1

The line is defined by two planes

• $x=0$
• $z = \frac{1}{\sqrt{2}}$

and a generic point P on the line is in the form $(0,t,\frac{1}{\sqrt{2}})=(0,0,\frac{1}{\sqrt{2}})+t(0,1,0)$ which is known as parametric form of the line equation $P(t)=P_0+t\vec v$ thus by definition the direction vector is $$\vec v=(0,1,0)$$

Answer 2

The line is in the $yz$ plain and is parallel to the $y$-axis. A vector parallel to the $y$-axis has its direction vector $\vec{j}$ which is the direction vector of the $y$-axis.