I find terms like into the plane of paper out of the plane of paper How am I supposed to understand that?
[Physics] Confusion regarding plane of the paper
homework-and-exercisesterminologyvectors
Related Solutions
Here's a quick sketch:
Gravity is the vector $u$. Its components in the plane and against the plane are $v$ and $w$ respectively. You want to find $v$.
The angle between the plane and horizontal is the same as the angle between $w$ and $u$, which allows you to find a simple trig relation to solve the problem.
Best Answer
A good example of where this kind of terminology is often used for electrical current go into or out of the page (or, as you wrote, into or out of the plane of the paper), as shown in the diagram below:
Image source: Evan's Space Wonders of Physics
(disclosure: not my website)
In summary - anything coming out of the page is heading out of the page perpendicular to the flat page (or the plane of the paper), the opposite is true for going into the page.