10. vector algebra — ગણિત ધોરણ 12 સાયન્સ — Question

હવે $j - k = a \times b = \left| {\begin{array}{*{20}{c}}   i&j&k \\    1&1&1 \\    {{b_1}}&{{b_2}}&{{b_3}}  \end{array}} \right|$

$\,{b_3} - {b_2} = 0,{b_1} - {b_3} = 1,{b_2} - {b_1} =  - 1$

$ \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$

આથી $b = i$