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