Mathematics - Vector Question with Solution | TestHub

$\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}\times \overrightarrow{\mathrm{a}}$ $\Rightarrow \overrightarrow{\mathrm{b}}\cdot \overrightarrow{\mathrm{c}}=0$ $\Rightarrow \left({\mathrm{b}}_1\hat{\mathrm{i}}+{\mathrm{b}}_2\hat{j}+{\mathrm{b}}_3\hat{\mathrm{k}}\right)\cdot (\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})=0$ ${\mathrm{b}}_1-{\mathrm{b}}_2-{\mathrm{b}}_3=0$ and $\overrightarrow{\mathrm{a}}\cdot \overrightarrow{\mathrm{b}}=3$ $\Rightarrow {\mathrm{b}}_2-{\mathrm{b}}_3=3$ ${\mathrm{b}}_1={\mathrm{b}}_2+{\mathrm{b}}_3=3+2{\mathrm{b}}_3$ $\overrightarrow{\mathrm{b}}=\left(3+2{\mathrm{b}}_3\right)\hat{\mathrm{i}}+\left(3+{\mathrm{b}}_3\right)\hat{\mathrm{j}}+{\mathrm{b}}_3\hat{\mathrm{k}}$