Question

(3) 9. (a) Let (21,91,2), B(22,92,-2),(3,3,3) be three non-collinear points in that is, three points which do not all lie on a straight line. Then the equations of the plane through these three points is: 30 Iii 0 12 32 22 3 Page 1 2 (b) Find the equation of the plane through (1,2,2), B(1,2-1), B(0,1,2)

Answer 1

by to + C2 rdzo o 9Y@Solution Let the equation of the required plane be ant by of the plane © Passess through theree non-cellimus points P ( xv, Y., 2.), (X1, X, 24) and P: (12, 79, 23), then, axit by te fit d = 0 al+by +67₂ +d=0 ax3 + b3 +C Zz+d=0 Elimin inating a,bed from 0, and 6 , we get, 2 X x M 5 =0. U2 N di cam ods 23 which is the required equation of the plane. This completes the proof of part 19 (a)

|9x1). Solution. The equation of the plane passing through the points P, (1,2,2), p (1,2,1) Pa (0,1,2) is given, using 6, by. R y 2 ch a id = 0 2 2-0 V-1 2-2 0 N 1 o o IR 2- Ri = R 0 -3 2 [R3-R4 = R3 O 22 > y-1 2-2 0 20 -3 co >> *(-3-0) -(4-1) (-3-0)+4-2)(1-1) = > -3x+3(3-1) = 0 = -x + y - l = 0 ie., 2-y+1=0 Therefore, the equation of the plane passing through genen Heree points is geren by. This completes the solution of [a (6)

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