art 1

The Sphere:In space, the collection of all points that are the same distance from some fixed point is

called a sphere.

See the illustration below. The constant distance is called the radius, and the fixed point is the center of the

sphere. Show that the equation of a sphere with the center at (x₀, y₀, z₀) and the radius r is

(x - x₀)²+ (y-y₀)²+ (z-z₀)²= r²

[Hint: Use the distance Formula.]

Part 2

Consider the following vectorsuandv: IF

and

what, if anything, can you conclude about the vectorsuandv?

Discuss your conclusion in detail.