Given three vectors ,

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Given three vectors a\mathbf{a} , b\mathbf{b} , c\mathbf{c} such that they are non-zero, non-coplanar vectors, then which of the following are coplanar. (1) a+b\mathbf{a} + \mathbf{b} , b+c\mathbf{b} + \mathbf{c} , c+a\mathbf{c} + \mathbf{a} (2) a−b\mathbf{a} - \mathbf{b} , b+c\mathbf{b} + \mathbf{c} , c+a\mathbf{c} + \mathbf{a} (3) a+b\mathbf{a} + \mathbf{b} , b−c\mathbf{b} - \mathbf{c} , c+a\mathbf{c} + \mathbf{a} (4) a+b\mathbf{a} + \mathbf{b} , b+c\mathbf{b} + \mathbf{c} , c−a\mathbf{c} - \mathbf{a}

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