$\,\vec c $ સાથે આદિશ ગુણાકાર લેતાં,
$\left( {\vec b \,\, - \,\,3\,\vec c } \right)\,\,.\,\vec c \,\, = \,\,\lambda \,\,\left( {\vec a .\,\vec c } \right)$
$ \Rightarrow \,\vec b .\,\vec c \,\, - \,\,3\,\left( {\vec c .\,\vec c } \right)\, = \,\,\lambda \,\,\left( {\vec a .\,\vec c } \right)$
$ \Rightarrow \,\,\vec b .\,\vec c \, - \,\,3\,\, = \,\,\lambda \,\,\,$ [${\because \,|\vec a |\,\, = \,\,|\vec c |\,\, = \,\,1}$ અને ${\vec a }$ અને ${\vec c }$ સમરેખ સદીશો છે ]
$ \Rightarrow \,\vec b .\,\vec c \,\, = \,\,3\,\, + \;\,\lambda $
ફરીથી $\vec b \,\, - \,\,\,3\,\vec c \,\, = \,\,\lambda \,\,\vec a $
$ \Rightarrow \,\,|\vec b \,\, - \,\,\,3\,\vec c |\,\, = \,\,\left| {\lambda \,\vec a } \right|$
$ \Rightarrow \,\,\,|\vec b \,\, - \,\,\,3\,\vec c {|^2}\, = \,\,{\lambda ^2}\,|\vec a {|^2}\,\,$
$ \Rightarrow \,\,\,|\vec b {|^2}\,\, + \,\,9\,|\vec c {|^2}\,\, - \,\,6\,\,\left( {\vec b .\,\,\vec c } \right)\,\, = \,\,{\lambda ^2}\,\,|\vec a {|^2}$
$ \Rightarrow \,\,36\,\, + \;\,9\,\, - \,\,6\,\,\left( {3\,\, + \;\,\lambda } \right)\,\, = \,\,{\lambda ^2}$
$ \Rightarrow \,\,27\,\, - \,\,6\lambda \,\, = \,\,{\lambda ^2}\,$
$ \Rightarrow \,\,{\lambda ^2}\,\, + \;\,6\lambda \,\, - \,\,27\,\, = \,\,0\,\, $
$\Rightarrow \,\,\lambda \,\, = \,\, - 9,\,3\,$
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| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ |
| $P(X)$ | $K^2$ | $2K$ | $K$ | $2K$ | $5K^2$ |
તો $\mathrm{P}(\mathrm{X}> 2)$ મેળવો.