JEE MAIN - Mathematics (2019 - 11th January Morning Slot - No. 4)
Let A = $$\left( {\matrix{
0 & {2q} & r \cr
p & q & { - r} \cr
p & { - q} & r \cr
} } \right).$$ If AAT = I3, then $$\left| p \right|$$ is :
$${1 \over {\sqrt 2 }}$$
$${1 \over {\sqrt 5 }}$$
$${1 \over {\sqrt 6 }}$$
$${1 \over {\sqrt 3 }}$$
Explanation
A is orthogonal matrix
$$ \Rightarrow $$ 02 + p2 + p2 = 1
$$ \Rightarrow $$ $$\left| p \right| = {1 \over {\sqrt 2 }}$$
$$ \Rightarrow $$ 02 + p2 + p2 = 1
$$ \Rightarrow $$ $$\left| p \right| = {1 \over {\sqrt 2 }}$$
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