WBJEE · Maths · Matrices
If the matrix \(\left(\begin{array}{ccc}0 & a & a \\ 2 b & b & -b \\ c & -c & c\end{array}\right)\) is orthogonal, then the values of \(a, b, c\) are
- A \(a= \pm \frac{1}{\sqrt{3}}, b= \pm \frac{1}{\sqrt{6}}, c= \pm \frac{1}{\sqrt{2}}\)
- B \(a= \pm \frac{1}{\sqrt{2}}, b= \pm \frac{1}{\sqrt{6}}, c= \pm \frac{1}{\sqrt{3}}\)
- C \(a=-\frac{1}{\sqrt{2}}, b=-\frac{1}{\sqrt{6}}, c=-\frac{1}{\sqrt{3}}\)
- D \(a=\frac{1}{\sqrt{3}}, b=\frac{1}{\sqrt{6}}, c=\frac{1}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(B) \(a= \pm \frac{1}{\sqrt{2}}, b= \pm \frac{1}{\sqrt{6}}, c= \pm \frac{1}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\begin{array}{ll}\text {} \vec{r}_1=0 \hat{i}+a \hat{j}+a \hat{k} & \vec{r}_1 \cdot \vec{r}_1=1 \Rightarrow 2 a^2=1 \\ \vec{r}_2=2 b \hat{i}+b \hat{j}-b \hat{k} & \vec{r}_2 \cdot \vec{r}_2=1 \Rightarrow 6 b^2=1 \\ \vec{r}_3=c \hat{i}-c \hat{j}+c \hat{k} & \vec{r}_3 \cdot…
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