Question

Let ${\bf{\vec a}},{\bf{\vec b}},{\bf{\vec c}}$ be three non-coplanar vectors and ${{\bf{\vec r}}}$ be any vector in space such that ${\bf{\vec r}}\cdot{\bf{\vec a}} = 1,{\rm{\;}}{\bf{\vec r}}\cdot{\bf{\vec b}} = 2{\rm{\;and}}\;{\bf{\vec r}}\cdot{\bf{\vec c}} = 3$. If $\left[ {{\rm{\;}}{\bf{\vec a}}\;{\bf{\vec b}}\;{\bf{\vec c}}{\rm{\;}}} \right] = 1$, then ${{\bf{\vec r}}}$ is equal to

Accepted Answer

${\bf{\vec b}} 	imes {\bf{\vec c}} + 2{\bf{\vec c}} 	imes {\bf{\vec a}} + 3{\bf{\vec a}} 	imes {\bf{\vec b}}$

Answer

${\bf{\vec a}} + 2{\bf{\vec b}} + 3{\bf{\vec c}}$

Answer

$\left( {\;{\bf{\vec b}}\cdot{\bf{\vec c}}\;} \right){\bf{\vec a}} + 2\left( {{\bf{\vec c}}\cdot{\bf{\vec a}}\;} \right){\bf{\vec b}} + 3\left( {\;{\bf{\vec a}}\cdot{\bf{\vec b}}} \right) + {\bf{\vec c}}$

Answer

None of these

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

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