MAT 21C Lecture Notes - Lecture 11: Cartesian Coordinate System, Scalar Multiplication, Unit Vector
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MAT 21C Full Course Notes
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Announcements: o ce hours: msb 3106 w1-2, f1-2. A point p in 3-dimensional space written in cartesian coordinates is p (x, y, z). They are the values at which the planes through p perpendicular to the axes cut the axes. The coordinate planes determined by the axes are: the xy-plane whose standard equation is z = 0, the yz-plane x = 0, and the xz-plane y = 0. They meet at the origin (0, 0, 0). The three coordinate planes x = 0, y = 0, z = 0 divided space into eight cells called octants. The standard equation for the sphere of radius r and center (x0, y0, z0) (x x0)2 + (y y0)2 + (z z0)2 = r2. The distance between p1(x1, y1, z1) and p2(x2, y2, z2) is. The midpoint of the line segment joining p1 to p2 is the point. |p1p2| = p(x2 x1)2 + (y2 y1)2 + (z2 z1)2 (cid:18) x1 + x2.
