If
a → , b → , c → \overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c a , b , c are three non-zero, non-coplanar vectors and
b 1 → = b → − b → . a → ∣ a → ∣ 2 a → , b 2 → = b → + b → . a → ∣ a → ∣ 2 a → , \overrightarrow {{b_1}} = \overrightarrow b - {{\overrightarrow b .\,\overrightarrow a } \over {{{\left| {\overrightarrow a } \right|}^2}}}\overrightarrow a ,\overrightarrow {{b_2}} = \overrightarrow b + {{\overrightarrow b .\,\overrightarrow a } \over {{{\left| {\overrightarrow a } \right|}^2}}}\overrightarrow a , b 1 = b − ∣ a ∣ 2 b . a a , b 2 = b + ∣ a ∣ 2 b . a a , c 1 → = c → − c → . a → ∣ a → ∣ 2 a → + b → . c → ∣ c ∣ 2 b → 1 , c 2 → = c → − c → . a → ∣ a → ∣ 2 a → − b → . c → ∣ b → 1 ∣ 2 b → 1 , \overrightarrow {{c_1}} = \overrightarrow c - {{\overrightarrow c .\,\overrightarrow a } \over {{{\left| {\overrightarrow a } \right|}^2}}}\overrightarrow a + {{\overrightarrow b .\,\overrightarrow c } \over {{{\left| c \right|}^2}}}{\overrightarrow b _1},\,\,\overrightarrow {{c_2}} = \overrightarrow c - {{\overrightarrow c .\,\overrightarrow a } \over {{{\left| {\overrightarrow a } \right|}^2}}}\overrightarrow a - {{\overrightarrow b \,.\,\overrightarrow c } \over {{{\left| {{{\overrightarrow b }_1}} \right|}^2}}}{\overrightarrow b _1}, c 1 = c − ∣ a ∣ 2 c . a a + ∣ c ∣ 2 b . c b 1 , c 2 = c − ∣ a ∣ 2 c . a a − b 1 2 b . c b 1 , c 3 → = c → − c → . a → ∣ c → ∣ 2 a → + b → . c → ∣ c ∣ 2 b → 1 , c 4 → = c → − c → . a → ∣ c → ∣ 2 a → − b → . c → ∣ b → 1 ∣ 2 b → 1 , \overrightarrow {{c_3}} = \overrightarrow c - {{\overrightarrow c .\,\overrightarrow a } \over {{{\left| {\overrightarrow c } \right|}^2}}}\overrightarrow a + {{\overrightarrow b .\,\overrightarrow c } \over {{{\left| c \right|}^2}}}{\overrightarrow b _1},\,\,\overrightarrow {{c_4}} = \overrightarrow c - {{\overrightarrow c .\,\overrightarrow a } \over {{{\left| {\overrightarrow c } \right|}^2}}}\overrightarrow a - {{\overrightarrow b \,.\,\overrightarrow c } \over {{{\left| {{{\overrightarrow b }_1}} \right|}^2}}}{\overrightarrow b _1}, c 3 = c − ∣ c ∣ 2 c . a a + ∣ c ∣ 2 b . c b 1 , c 4 = c − ∣ c ∣ 2 c . a a − b 1 2 b . c b 1 , then the set of orthogonal vectors is