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Let \( P_{1} \) denote the equation of a plane to which the vector \( (\hat{i}+\hat{j}) \) is normal and which contains the line whose equation is \( \vec{r}=\hat{i}+\hat{j}+\hat{k}+\lambda(\hat{i}-\hat{j}-\hat{k}) \) and \( P_{2} \) denote the equation of the plane containing
\( \mathrm{P} \) the line \( L \) and a point with position vector \( \hat{j} \). Which of the following holds good?

W
(1) The equation of \( P_{1} \) is \( x+y=2 \).
(2) The equation of \( P_{2} \) is \( \vec{r} \cdot(\hat{i}-2 \hat{j}+\hat{k})=2 \)
(3) The acute angle between \( P_{1} \) and \( P_{2} \) is \( \cot ^{-1}(\sqrt{3}) \).
(4) The angle between the plane \( P_{2} \) and the line \( L \) is \( \tan ^{-1} \sqrt{3} \).
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