JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\, = \,\left( {\begin{array}{*{20}{c}}
0&{2q}&r\\
p&q&{ - r}\\
p&{ - q}&r
\end{array}} \right)\). If \(A{A^T}\, = \,{I_3},\,\left| p \right|\) then \(\left| p \right|\) is
- A \(\frac{1}{{\sqrt 5 }}\)
- B \(\frac{1}{{\sqrt 3 }}\)
- C \(\frac{1}{{\sqrt 2 }}\)
- D \(\frac{1}{{\sqrt 6 }}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{{\sqrt 2 }}\)
Step-by-step Solution
Detailed explanation
\(A\) is orthogonal matrix \(\therefore 4{q^2} + {r^2} = {p^2} + {q^2} + {r^2} = 1\,\,\,\,\,\,.......\left( 1 \right)\) \({p^2} - {q^2} - {r^2} = 0\,\,\,\,\,\,...\left( 2 \right)\) and \(2{q^2} - {r^2} = 0\,\,\,\,\,....\left( 3 \right)\) Solving \((1),(2)\) and \((3)\)…
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