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Question

Show that the four points A(4,5,1),B(0,1,1),C(3,9,4) and D(4,4,4) are coplanar.

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Solution

For the four points A,B,C,D to be coplanar , they should lie on same plane which implies AD.(AC×AB)=0
AB=4i+6j+2k , AC=i4j3k and AD=8i+j3k
AB×AC=i(18+8)+j(2+12)+k(166)=10i+14j22k
AD.(AB×AC)=(8i+j3k).(10i+14j22k)=80+14+66=0
Therefore points A,B,C,D are coplanar.

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