Stuck on a few Vector homework problems

[PhantomDiclonius]

Homework Statement

Write out the vectors A+B and A-B in terms of the unit vectors i and j. Show them on your coordinate system.

Use the Right-Hand-Rule to determine the direction of the following:

Determine Speed and Direction with respect to the Earth.

Relevant Equations

[(A)^2 + (B)^2]

ArcTan = (Y/X)

ixj, ixk, jxk, ixi

I'm stuck on a few Vector homework problems. I don't quite understand how to write vectors A+B and A-B for questions 1b and 2b. I tried starting with calculating the magnitude for vector A+B on question 1b and then followed by finding theta, but I'm not sure if that's what I'm supposed to do.

I'm also completely flabbergasted by problem 4 where I'm supposed to use the Right-Hand-Rule to the direction of vectors such as i x i, how am I supposed to determine the direction if the vectors have no values?

Lastly, I'm pretty lost with question 5. I thought I did 5a correctly, but the part that asks "with respect to the Earth" makes me feel uneasy. I don't understand how to calculate something with respect to the Earth, I just tried calculating the barge in comparison to the river speed the best that I could.

Sorry, this is my first week in Physics and I'm feeling pretty lost, any help would be greatly appreciated, here's a pic of the worksheet and my work so far, thank you for your time:

 

[berkeman]

Welcome to the PF.

I'm stuck on a few Vector homework problems. I don't quite understand how to write vectors A+B and A-B for questions 1b and 2b. I tried starting with calculating the magnitude for vector A+B on question 1b and then followed by finding theta, but I'm not sure if that's what I'm supposed to do.

Let's take these questions one at a time. Please show us your work adding the components of the first vectors, then we can go on to your other questions. Thanks.