Q27 of 36 Page 10

Show that the four points A (4, 5, 1), B(0, - 1, - 1), C(3, 9, 4) and D( - 4, 4, 4) are coplanar.[CBSE 2016]

We can write A,B,C and D as


AB = - 4i - 6j - 2k


AC = - i + 4j + 3k


AD = - 8i + j + 3k


If |AB AC AD | = 0 then ABCD are coplanar


∴


⇒ - 4(12 + 3) + 6( - 3 + 24) - 2(1 + 32)


⇒ - 60 + 126 - 66


= 0


∴ ABCD are coplanar.

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