Question

The equation of the plane passing through three non-collinear points ${\bf{\vec a}},{\bf{\vec b}},{\bf{\vec c}}$ is

Accepted Answer

${\bf{\vec r}}\cdot\left( {{\bf{\vec b}} 	imes {\bf{\vec c}} + {\bf{\vec c}} 	imes {\bf{\vec a}} + {\bf{\vec a}} 	imes {\bf{\vec b}}} ight) = \left[ {{\bf{\vec a}}\;{\bf{\vec b}}\;{\bf{\vec c}}} ight]$

Answer

${\bf{\vec r}}\cdot\left( {{\bf{\vec b}} 	imes {\bf{\vec c}} + {\bf{\vec c}} 	imes {\bf{\vec a}} + {\bf{\vec a}} 	imes {\bf{\vec b}}} ight) = 0$

Answer

${\bf{\vec r}}\cdot\left( {{\bf{\vec a}} 	imes \left( {{\bf{\vec b}} 	imes {\bf{\vec c}}} ight)} ight) = \left[ {{\bf{\vec a}}\;{\bf{\vec b}}\;{\bf{\vec c}}} ight]$

Answer

${\bf{\vec r}}\cdot\left( {{\bf{\vec a}} + {\bf{\vec b}} + {\bf{\vec c}}} \right) = 0$

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

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