Let $\overrightarrow a = 2\widehat i + {\lambda _1}\widehat j + 3\widehat k,\,\,$ $\overrightarrow b = 4\widehat i + \left( {3 - {\lambda _2}} \right)\widehat j + 6\widehat k,$ and $\overrightarrow c = 3\widehat i + 6\widehat j + \left( {{\lambda _3} - 1} \right)\widehat k$ be three vectors such that $\overrightarrow b = 2\overrightarrow a $ and $\overrightarrow a $ is perpendicular to $\overrightarrow c $. Then a possible value of $\left( {{\lambda _1},{\lambda _2},{\lambda _3}} \right)$ is :
(1, 5, 1)
(1, 3, 1)
$\left( { - {1 \over 2},4,0} \right)$
$\left( {{1 \over 2},4, - 2} \right)$
Solution
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