If the vector OA, ob, OC, OD satisfies: OA = xob + yoc + Zod (x, y, Z belong to R) and X + y + Z = 1, then a, B, C, D are coplanar

OA=xOB+yOC+zOD
x+y+z=1
So OA = xob + yoc + (1-x-y) od
Oa-od = x (ob-od) + y (oc-od)
DA=xDB+yDC
From the fundamental theorem of coplanar vector
Vector Da, DB, DC coplanar
And because these three vectors have a common point D
So a, B, C, D are coplanar

If the vector OA, ob, OC, OD satisfies: OA = xob + yoc + Zod (x, y, Z belong to R) and X + y + Z = 1, then a, B, C, D are coplanar

If the vector OA, ob, OC, OD satisfies: OA = xob + yoc + Zod (x, y, Z belong to R) and X + y + Z = 1, then a, B, C, D are coplanar

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