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Let vec a,vec b,vec c be three vectors i...

Let `vec a,vec b,vec c` be three vectors in the xyz space such that `vec a times vec b=vec b timesvec c=vec c timesvec a!=0` If `A,B,C` are points with position vectors `vec a,vec b,vec c` respectively,then the number of possible positions of the centroid of triangle `ABC` is (A) 1 (B) 2 (C) 3 (D) 6

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