Three vectors A, B, and C add up to zero. Find which is false a) vector (A×B)C is not zero unless vectors B, C are parallel d) vector (A×B).C is not zero unless vectors B, C are parallel c) if vectors A, B, C define a plane, (A×B)C is in that plane (A×B).C =  such that C2 = A2 + B2
The correct option is B. It is given that A+B+C=0 Now if vector triple product of A and B and C, then vector will always lie on the plane which will be formed by A,B and C. It means A+B+C=0 will always lie in a single plane forming sides of triangle. First take A×B=B×C Taking dot product with C on both side of above equation. (A×B)⋅C=(B×C)⋅C Now this will be zero on two conditions. First is that B and C are parallel to each other. But it could be zero without C being parallel to B. As when we will take the cross product of B and C vectors, then any vector perpendicular (say P) to both B and C. Then by taking the dot product of P and C will also be zero as the angle between them will always be 90 degrees. So, statement B is false.
