1. ## Few 3d problems

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.

2. Originally Posted by Ideasman
1.) I have to determine the geometric shape that is described by:

(x - 1)^2 + y^2 + (z + 2)^2 = 4
Consider,
$\displaystyle x^2+y^2+z^2=2^2=4$
This is a sphere with radius 2 at the origin.
But instead you have a translation,
$\displaystyle x\to x-1$ (moved 1 unit to the x positive direction)
$\displaystyle y\to y$ (unchanged)
$\displaystyle z\to z+2$ (moved 2 units to the z negative direction.

Thus, it is the same sphere centered at,
$\displaystyle (1,0,-2)$