8. The distance from a point Xo = (xo, Yo, zo) to a plane II in R3 is defined to be dist (:1:0, II) := { ~1111 :1:0 E II

:1:0 t/c II, where 11:= (xo - Xl, Yo - YI, Zo - Zl) for some (Xl. Yl. Zl) E II, and 11 is orthogonal to II, i.e., parallel to its normal. Sketch II and:l:o for a typical plane II, and convince yourself that this is the correct definition. Prove that this definition does not depend on the choice of 11, by showing that the distance from:l:o =

(xo, Yo, zo) to the plane II described by ax + by + cz = d is d1· st (: 1:0, II) = laxov +a byo + CZo - dl . 2 +b2 +c2