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Which of the following is an orthogonal matrix
$\left[ {\begin{array}{*{20}{c}}{6/7}&{2/7}&{ - 3/7}\\{2/7}&{3/7}&{6/7}\\{3/7}&{ - 6/7}&{2/7}\end{array}} \right]$
$\left[ {\begin{array}{*{20}{c}}{6/7}&{2/7}&{3/7}\\{2/7}&{ - 3/7}&{6/7}\\{3/7}&{6/7}&{ - 2/7}\end{array}} \right]$
$\left[ {\begin{array}{*{20}{c}}{ - 6/7}&{ - 2/7}&{ - 3/7}\\{2/7}&{3/7}&{6/7}\\{ - 3/7}&{6/7}&{2/7}\end{array}} \right]$
$\left[ {\begin{array}{*{20}{c}}{6/7}&{ - 2/7}&{3/7}\\{2/7}&{2/7}&{ - 3/7}\\{ - 6/7}&{2/7}&{3/7}\end{array}} \right]$
Solution
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
$\sum {a_i^2} \, = \,\sum {b_i^2} \, = \,\sum {c_i^2} \, = \,1$; $\sum {a_i\,b_i} = \sum {b_i\, c_i} = \sum {c_i\,a_i} = 0$
Similar Questions
Match the Statements / Expressions in Column $I$ with the Statements / Expressions in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ The minimum value of $\frac{x^2+2 x+4}{x+2}$ is | $(p)$ $0$ |
| $(B)$ Let $A$ and $B$ be $3 \times 3$ matrices of real numbers, where $A$ is symmetric, $B$ is skewsymmetric, and $(A+B)(A-B)=(A-B)(A+B)$. If $(A B)^t=(-1)^k A B$, where $(A B)^t$ is the transpose of the matrix $A B$, then the possible values of $k$ are | $(q)$ $1$ |
| $(C)$ Let $\mathrm{a}=\log _3 \log _3 2$. An integer $\mathrm{k}$ satisfying $1<2^{\left(-k+3^{-2}\right)}<2$, must be less than | $(r)$ $2$ |
| $(D)$ If $\sin \theta=\cos \phi$, then the possible values of $\frac{1}{\pi}\left(\theta \pm \phi-\frac{\pi}{2}\right)$ are | $(s)$ $3$ |
