Which of the following is an orthogonal matrix - Vidyadip

MCQ

Which of the following is an orthogonal matrix

✓
$\left[ {\begin{array}{*{20}{c}}{6/7}&{2/7}&{ - 3/7}\\{2/7}&{3/7}&{6/7}\\{3/7}&{ - 6/7}&{2/7}\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}{6/7}&{2/7}&{3/7}\\{2/7}&{ - 3/7}&{6/7}\\{3/7}&{6/7}&{ - 2/7}\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}{ - 6/7}&{ - 2/7}&{ - 3/7}\\{2/7}&{3/7}&{6/7}\\{ - 3/7}&{6/7}&{2/7}\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}{6/7}&{ - 2/7}&{3/7}\\{2/7}&{2/7}&{ - 3/7}\\{ - 6/7}&{2/7}&{3/7}\end{array}} \right]$

✓

Answer

Correct option: A.

$\left[ {\begin{array}{*{20}{c}}{6/7}&{2/7}&{ - 3/7}\\{2/7}&{3/7}&{6/7}\\{3/7}&{ - 6/7}&{2/7}\end{array}} \right]$

a
Matrix $\left[ {\,\begin{array}{*{20}{c}}{{a_1}}&{{a_2}}&{{a_3}}\\{{b_1}}&{{b_2}}&{{b_3}}\\{{c_1}}&{{c_2}}&{{c_3}}\end{array}\,} \right]$ is orthogonal if

$\sum {a_i^2} \, = \,\sum {b_i^2} \, = \,\sum {c_i^2} \, = \,1$; $\sum {a_i\,b_i} = \sum {b_i\, c_i} = \sum {c_i\,a_i} = 0$

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