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Question Number 140502 by benjo_mathlover last updated on 08/May/21

$$\mathrm{If}\mathrm{three}\mathrm{vector}\overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}}\mathrm{and}\overrightarrow{\mathrm{c}}\mathrm{are}$$$$\mathrm{such}\mathrm{that}\overrightarrow{\mathrm{a}}\ne 0\mathrm{and}\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}=2\left(\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{c}}\right)$$$$,\mid \overrightarrow{\mathrm{a}}\mid =\mid \overrightarrow{\mathrm{c}}\mid =1,\mid \overrightarrow{\mathrm{b}}\mid =4\mathrm{and}\mathrm{the}$$$$\mathrm{angle}\mathrm{between}\overrightarrow{\mathrm{b}}\mathrm{and}\overrightarrow{\mathrm{c}}\mathrm{is}{\cos }^{-1}\left(\frac{1}{4}\right),$$$$\mathrm{then}\overrightarrow{\mathrm{b}}-2\overrightarrow{\mathrm{c}}=\lambda \overrightarrow{\mathrm{a}},\mathrm{where}\lambda =?$$

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