Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems 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} α ( a × b ) + β ( b × c ) + γ ( c × a ) = 0
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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} α ( a × b ) + β ( b × c ) + γ ( c × a ) = 0 a \mathbf{a} a b \mathbf{b} b c \mathbf{c} c α \alpha α β \beta β γ ≠ 0 \gamma \neq 0 γ = 0 a \mathbf{a} a b \mathbf{b} b c \mathbf{c} c α \alpha α β \beta β γ = 0 \gamma = 0 γ = 0 a \mathbf{a} a b \mathbf{b} b c \mathbf{c} c α \alpha α β \beta β γ \gamma γ Browse the problem library