MCQ
જો $\vec a \, = \,\,i\,\, + \;\,j\,\, + \;\,k$ અને $\vec a .\,\vec b \, = \,\,1\,$ અને $\vec a \times \,\,\vec b \,\, = \,\,j\,\, - \,\,k\,\,$ તો $\vec b \, = \,.....$
- A$2i$
- B$i - j + k$
- C$i$
- D$2j - k$
હવે,$\,j - k\,\, = \, a\, \times \,\,b\,\, = \,\,\left| {\,\begin{array}{*{20}{c}} i&j&k \\ 1&1&1 \\ {{b_1}}&{{b_2}}&{{b_3}} \end{array}\,} \right|\,$
$ \Rightarrow \,\,\,{b_3} - {b_2} = 0\,,\,{b_1} - {b_3} = \,\,1\,,\,\,{b_2} - {b_1} = \,\, - 1\,\,\, $
$\Rightarrow \,\,{b_3} = \,\,{b_2}\,,\,\,{b_1} = \,\,{b_2} + 1$
હવે,$a\,.\,\,b\,\, = \,\,1\,\, \Rightarrow \,\,{b_1} + {b_2} + {b_3} = 1$
$ \Rightarrow \,\,\,3{b_2} + 1 = \,\,1\,\, \Rightarrow \,\,{b_2} = 0\,\, \Rightarrow \,\,{b_1} = \,\,1\,,\,\,{b_3} = 0\,.$
તેથી$,\,\,b\,\, = \,\,i.$
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