Q68 / 160 · AP EAMCET 2015 · Mathematics

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

  • A
    $0$
  • Correct answer
    B
    $1$
  • C
    $2$
  • D
    $3$

Solution

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 $\begin{aligned} & {[\mathrm{a} \times \mathrm{b} \quad \mathrm{b} \times \mathrm{c} \quad \mathrm{c} \times \mathrm{a}]=[\mathrm{ab} \mathrm{c}]^2} \\ & \therefore \quad \lambda=1 \end{aligned}$

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

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