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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
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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