name all the conditions for the coplanarity of three vectors and four vectors,similarly for the collinearity of three vectors and four vectors???

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cosinusix | College Teacher | (Level 3) Assistant Educator

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3 vectors of RR^3  are coplanar iff their deteminant is 0

3 vectors `vecA, vecB, vecC` are coplanar iff there exists a triplet `(a,b,c)ne(0,0,0)` such that  `avecA+bvecB+cvecC=vec0`

4 vectors are coplanar iff the determinant of any 3 of the vectors is 0.

4 vectors`` are coplanar iff any 3 of the vectors are coplanar

iff any 3 of the vectors, written  `vecA,vecB,vecC` there exists (a,b,c)ne(0,0,0) such that `avecA+bvecB+cvecC=0`

 

 


3 or 4 vectors are collinear iff any 2 of the vectors `vecA,` `vecB` satisfy: there exist `(a,b)ne(0,0)` such that `avecA+bvecB=vec0 ` .

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