If and are three non-coplanar vectors

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

Problem

If u,v\mathbf{u}, \mathbf{v} and w\mathbf{w} are three non-coplanar vectors, then (u+v−w)⋅[(u−v)×(v−w)](\mathbf{u} + \mathbf{v} - \mathbf{w}) \cdot [(\mathbf{u} - \mathbf{v}) \times (\mathbf{v} - \mathbf{w})] equal to (1) 0 (2) u⋅v×w\mathbf{u} \cdot \mathbf{v} \times \mathbf{w} (3) u⋅w×v\mathbf{u} \cdot \mathbf{w} \times \mathbf{v} (4) 3u⋅v×w3\mathbf{u} \cdot \mathbf{v} \times \mathbf{w}

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