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Values of $a, b$ and $c$, which render the matrix $Q=\left[\begin{array}{lll}\frac{1}{\sqrt{3}} & \frac{1}{\sqrt{2}} & a \\ \frac{1}{\sqrt{3}} & 0 & b \\ \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{2}} & c\end{array}\right]$ orthonormal are, respectively
(A) $\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0$
(B) $\frac{1}{\sqrt{6}},-\frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}$
(C) $-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$
(D) $-\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}},-\frac{1}{\sqrt{6}}$


Question ID - 156022 | Toppr Answer

Values of $a, b$ and $c$, which render the matrix $Q=\left[\begin{array}{lll}\frac{1}{\sqrt{3}} & \frac{1}{\sqrt{2}} & a \\ \frac{1}{\sqrt{3}} & 0 & b \\ \frac{1}{\sqrt{3}} & -\frac{1}{\sqrt{2}} & c\end{array}\right]$ orthonormal are, respectively
(A) $\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0$
(B) $\frac{1}{\sqrt{6}},-\frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}$
(C) $-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$
(D) $-\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}},-\frac{1}{\sqrt{6}}$

1 Answer - 5876 Votes

3537

Answer Key : (D) -

(D) $-\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}},-\frac{1}{\sqrt{6}}$



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