1.) I have to determine the geometric shape that is described by:

(x - 1)^2 + y^2 + (z + 2)^2 = 4

2.) How do I identify a plane that is parallel to the xy-plane, xz-plane or the yz-plane, given

y = 4, and then:

z = -1

I'm assuming, based on the answers in the back of the book, if you're given a specific coordinate, then that is parallel to the other two planes, that is, if given y = 4 then that's parallel to the xz-plane and when given z = -1 that's parallel to the xy-plane, but why?

Then, it asks for me to sketch a graph.

3.) Determine the angle between the two given vectors:

a = 3i + j - 4k; b = -2i + 2j + k

I'm assuming you use ||a||*||b||cos(theta) ... so find the norm of each of the vectors and then multiply them and then finally find the arccos of that?

Thanks.