MCQ
If $a,b,c$ are three non-zero, non-coplanar vectors and
${{b}_{1}}=b-\frac{b.a}{|a{{|}^{2}}}a,\,{{b}_{2}}=b+\frac{b.a}{|a{{|}^{2}}}a$ , ${{b}_{1}}=b-\frac{b.a}{|a{{|}^{2}}}a,\,{{b}_{2}}=b+\frac{b.a}{|a{{|}^{2}}}a$
, ${{c}_{2}}=c-\frac{c.a}{|a{{|}^{2}}}a-\frac{c.{{b}_{1}}}{|{{b}_{1}}{{|}^{2}}}{{b}_{1}}$
,${{c}_{3}}=c-\frac{c.a}{|a{{|}^{2}}}a-\frac{c.{{b}_{2}}}{|{{b}_{2}}{{|}^{2}}}{{b}_{2}}$,
${{c}_{4}}=a-\frac{c.a}{|a{{|}^{2}}}a$.
Then which of the following is a set of mutually orthogonal vectors is
- A$\{{a},\,{b_{1}},\,{{c}_{1}}\}$
- ✓$\{{a},\,{b_{1}},\,{{c}_{2}}\}$
- C$\{{a},\,{b_{2}},\,{{c}_{3}}\}$
- D$\{{a},\,{b_{2}},\,{{c}_{4}}\}$