What is the Direction of A X B Using the Right Hand Rule?

[belvol16]

Homework Statement

The direction of vectors A and B are given below for several cases. For each case, state the direction of A X B.
a) A points east, B points south.
b) A points east, B points straight down.
c) A points straight up, B points north.
d) A points straight up, B points straight down.

Homework Equations

Using the right hand rule.

The Attempt at a Solution

So, I've tried to use the right hand rule but I am not sure if I am using it properly. (I haven't taken multivariable calculus yet so I struggle with dot products and vector cross products). I used my pointer finger as my x-axis, middle finger as my y-axis, and thumb as my z-axis.
a) I found that the vector points into the page. I put my index finger towards the east and middle finger south and found that my thumb pointed into my page.
b) I guess I'm not sure if pointing straight down is different than pointing south. If pointing straight down is the same as south, then b) points into the page as well.
c) I'm a little bit confused. I took both my index finger and middle finger and pointed them up and found the resultant vector points into the page.
d) I stuck my pointer finger up and middle finger down and found that the resultant vector points into the page.
I guess I don't quite understand how all of these vectors point into the page or if I'm doing something wrong. I've watched a few other tutorials using a method where you curl your fingers, but I didn't quite understand how those worked.
Any help is greatly appreciated.

 

[phyzguy]

I think you should view it as a map laying on a table. So there are three orthogonal axes - (1) east - west, (2) north-south, (3) up-down. So down is not in the same direction as south. So I would use up-down instead of into and out of the page, because it is less confusing.

 

[TSny]

I agree with phyzguy. Imagine that you are standing outside on level ground. N, S, E, and W would be directions parallel to the ground. "Straight up" would be vertically upward, perpendicular to the ground. "Straight down" would be vertically downward, perpendicular to the ground.

 

[Charles Link]

I never used my fingers on the right hand rule for a vector cross-product. Instead, I envision a jar with a lid with a right-hand screw (right-hand is standard on all jars), and which way the cap moves (up or down) when you rotate it=e.g. rotating one vector into the other.