IB Diploma Programme

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

If α(a×b)+β(b×c)+γ(c×a)=0\alpha(\mathbf{a} \times \mathbf{b}) + \beta(\mathbf{b} \times \mathbf{c}) + \gamma(\mathbf{c} \times \mathbf{a}) = \mathbf{0} , then (1) a\mathbf{a} , b\mathbf{b} , c\mathbf{c} are coplanar if all of α\alpha , β\beta , γ≠0\gamma \neq 0 (2) a\mathbf{a} , b\mathbf{b} , c\mathbf{c} are coplanar if any one α\alpha , β\beta , γ=0\gamma = 0 (3) a\mathbf{a} , b\mathbf{b} , c\mathbf{c} are non-coplanar for any α\alpha , β\beta , γ\gamma (4) None of the above

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