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Which of the following is an orthogonal ...

Which of the following is an orthogonal matrix ? ( ⎡ ⎢ ⎣ 6 / 7 2 / 7 − 3 / 7 2 / 7 3 / 7 6 / 7 3 / 7 − 6 / 7 2 / 7 ⎤ ⎥ ⎦ (b) ⎡ ⎢ ⎣ 6 / 7 2 / 7 3 / 7 2 / 7 − 3 / 7 6 / 7 3 / 7 6 / 7 − 2 / 7 ⎤ ⎥ ⎦ (c) ⎡ ⎢ ⎣ − 6 / 7 − 2 / 7 − 3 / 7 2 / 7 3 / 7 6 / 7 − 3 / 7 6 / 7 2 / 7 ⎤ ⎥ ⎦ (d) ⎡ ⎢ ⎣ 6 / 7 − 2 / 7 3 / 7 2 / 7 2 / 7 − 3 / 7 − 6 / 7 2 / 7 3 / 7 ⎤ ⎥ ⎦

A

`[(6//7,2//7,-3//7),(2//7,3//7,6//7),(3//7,-6//7,2//7)]`

B

`[(6//7,2//7,3//7),(2//7,-3//7,6//7),(3//7,6//7,-2//7)]`

C

`[(-6//7,-2//7,-3//7),(2//7,3//7,6//7),(-3//7,6//7,2//7)]`

D

`[(6//7,-2//7,3//7),(2//7,2//7,-3//7),(-6//7,2//7,3//7)]`

Text Solution

Verified by Experts

The correct Answer is:
A
Matrix `[(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))]` is orthogonal if
`sum a_(i)^(2)=sum b_(i)^(2)=sum c_(i)^(2)=1, sum a_(i)b_(i)=sum b_(i)b_(i)=sum c_(i)a_(i)=0`
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