\[{\text{P}} = {\left[ {\begin{array}{{20}{c}} { - 10} \\ { - 1} \\ 3 \end{array}} \right]^{\text{T}}},{\text{Q}} = {\left[ {\begin{array}{{20}{c}} { - 2} \\ { - 5} \\ 9 \end{array}} \right]^{\text{T}}}\] and \[{\text{R}} = {\left[ {\begin{array}{*{20}{c}} 2 \\ { - 7} \\ {12} \end{array}} \right]^{\text{T}}}\] are three vectors. An orthogonal set of vectors having a span that contains P, Q, R is

A) \[\left[ {\begin{array}{*{20}{c}} { - 6} \\ { - 3} \\ 6 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 4 \\ { - 2} \\ 3 \end{array}} \right]\] B) \[\left[ {\begin{array}{*{20}{c}} { - 4} \\ 2 \\ 4 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 5 \\ 7 \\ { - 11} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 8 \\ 2 \\ { - 3} \end{array}} \right]\] C) \[\left[ {\begin{array}{*{20}{c}} 6 \\ 7 \\ { - 1} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} { - 3} \\ 2 \\ { - 2} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 3 \\ 9 \\ { - 4} \end{array}} \right]\] D) \[\left[ {\begin{array}{*{20}{c}} 4 \\ 3 \\ {11} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1 \\ {31} \\ 3 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 5 \\ 3 \\ 4 \end{array}} \right]\]

Answer & Solution

Correct Answer: Option A

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