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Let \( \Pi: x+y-z-4=0 \) be the equation of a plane and \( A \) be the point with position vector \( \hat{i}+2 \hat{j}-3 \hat{k} \). L is a line which passes through the point \( (1,2,3) \) with direction ratios \( 3,-1 \) and 4 . If
\( \mathrm{P} \) the distance of the point A from the line \( \mathrm{L} \) measured parallel to the plane \( \Pi \) is \( \mathrm{d}_{1} \) and the distance

W of the point \( \mathrm{A} \) from the plane \( \Pi \) measured parallel to the line \( \mathrm{L} \) is \( \mathrm{d}_{2} \), then find the value of
\[
\sqrt{\mathrm{d}_{1}^{2}-\mathrm{d}_{2}^{2}}
\]
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