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Engineering Maths · Q60

Linear Algebra

Engineering and GATE · Engineering Maths · question 60

Q60

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

{\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]
Answer
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: Option A

Solution

Answer: Option A
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