MATH 226 Lecture 2: Math Lecture 2
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Equation of a sphere of radius r centered at c (a, b, c) A sphere is the set of points m= (x, y, z)that are r units from c. What do you get when intersecting that sphere with the plane x=2? (x+1)2 + (y-3)2 + (z+4)2 -1 -9 -16 = 2 (x+1)2 + (y-3)2 + (z+4)2 = 28 center = (-1, 3, -4) A circle in the plane x=2 with radius of < 2 (cid:889) Plug in x=2 into the equation of the sphere (2+1)2 + (y-3)2 + (z+4)2 = 28 (y-3)2 + (z+4)2 = 19. Whenever you intersect, you get a curve or a finite set of points. Remark: what is the surface described by (y-3)2 + (z+4)2 = 19. It must be restricted to a plane to be a circle like how in example two it is. A parabola that extends up along the z axis. A vector in the third dimension is given by:
