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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.
Solution
Given points are A(4, 5, 1), B(0, –1, –1), C(3, 9, 4) and D(–4, 4, 4).
`∴ vec(AB) = (-4hati - 6hatj - 2hatk)`
`vec(AC) = (-hati + 4hatj + 3hatk)`
`vec(AD) = (-8hati + hatj + 3hatk)`
`∴ [(vec(AB), vec(AC), vec(AD))] = |(-4, -6, -2),(-1, 4, 3),(-8, -1, 3)|`
= – 4(12 + 3) + 6(– 3 + 24) – 2(1 + 32)
= – 60 + 126 – 66
= 0
∴ Four points A, B, C, D are coplannar.
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