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Let $A = (\begin{matrix} 0 & 2 b & c \\ a & b & - c \\ a & - b & c \end{matrix})$ be an orthogonal matrix then the values of a, b, c are

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a

b=±16,c=±13

b

a=±12,c=±16

c

a=±12,b=±16

d

All of these

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detailed solution

Correct option is D

A=02bcab-ca-bcand A'=0aa2bb-bc-ccAs A is orthogonal∴ AA′ = I⇒02bcab-ca-bc0aa2bb-bc-cc=100010001⇒4b2+c22b2-c2-2b2+c22b2-c2a2+b2+c2a2-b2-c2-2b2+c2a2-b2-c2a2+b2+c2 =100010001∴ Using definition of equality of two matrices4b2+c2=1,2b2-c2=0,a2+b2+c2=1On solving them,a=±12,b=±16,c=+13

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