If a(α × β)+b(β × γ)+c(γ × α)=overrightarrow0 , where a, b, c are non-zero scalars, then the vectors α, β, γ are

Correct answer: (C) coplanar. ∴ α × β, β × λ, γ × α are coplanar ⇒ α, β, γ are coplanar

Q95 / 155 · WBJEE 2021 · Mathematics

If $\mathrm{a}(\vec{\alpha} \times \vec{\beta})+\mathrm{b}(\vec{\beta} \times \vec{\gamma})+\mathrm{c}(\vec{\gamma} \times \vec{\alpha})=\overrightarrow{0}$, where $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are non-zero scalars, then the vectors $\vec{\alpha}, \vec{\beta}, \vec{\gamma}$ are

A
parallel
B
non-coplanar
Correct answer
C
coplanar
D
mutually perpendicular

Solution

$\therefore \vec{\alpha} \times \vec{\beta}, \vec{\beta} \times \vec{\lambda}, \vec{\gamma} \times \vec{\alpha}$ are coplanar $\Rightarrow \vec{\alpha}, \vec{\beta}, \vec{\gamma}$ are coplanar

Hence, the correct answer is option: 'C'.

If $\mathrm{a}(\vec{\alpha} \times \vec{\beta})+\mathrm{b}(\vec{\beta} \times \vec{\gamma})+\mathrm{c}(\vec{\gamma} \times \vec{\alpha})=\overrightarrow{0}$, where $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are non-zero scalars, then the vectors $\vec{\alpha}, \vec{\beta}, \vec{\gamma}$ are

Solution

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