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If $[\mathbf{a} \times \mathbf{b} \mathbf{b} \times \mathbf{c} \mathbf{c} \times \mathbf{a}]=\lambda[\mathbf{a} \mathbf{b} \mathbf{c}]^2$, then $\lambda$ is equal to
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Verified Answer
The correct answer is:
$1$
Given,
$[\mathrm{a} \times \mathrm{b} \quad \mathrm{b} \times \mathrm{c}\ c \times \mathrm{a}]=\lambda[\mathrm{abc}]^2$
As we know, the properties of cross product of three vectors, we have
$\begin{aligned}
& {[\mathrm{a} \times \mathrm{b} \quad \mathrm{b} \times \mathrm{c} \quad
\mathrm{c} \times \mathrm{a}]=[\mathrm{ab} \mathrm{c}]^2} \\
& \therefore \quad \lambda=1
\end{aligned}$
$[\mathrm{a} \times \mathrm{b} \quad \mathrm{b} \times \mathrm{c}\ c \times \mathrm{a}]=\lambda[\mathrm{abc}]^2$
As we know, the properties of cross product of three vectors, we have
$\begin{aligned}
& {[\mathrm{a} \times \mathrm{b} \quad \mathrm{b} \times \mathrm{c} \quad
\mathrm{c} \times \mathrm{a}]=[\mathrm{ab} \mathrm{c}]^2} \\
& \therefore \quad \lambda=1
\end{aligned}$
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