Consider two fixed points \( A(1,0,0) \) and \( P(1,0,1) \). If \( O A \) (where \( O \) is or...

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Consider two fixed points \( A(1,0,0) \) and \( P(1,0,1) \). If \( O A \) (where \( O \) is origin) is rotated through \( O \) in \( x y \)-plane by a variable angle \( \theta \), to reach a new position \( O B \), then which of the following statement (s) is (are) correct?
(a) Maximum volume of tetrahedron OAPB is \( \frac{1}{6} \)
(b) Maximum volume of tetrahedron OAPB is unity.
(c) The distance of plane \( O P B \) from point \( A \) is \( \frac{|\sin \theta|}{\sqrt{\left(1+\sin ^{2} \theta\right)}} \).
(d) Equation of the plane \( O P B \) is \( (z-x) \sin \theta+y \cos \theta=0 \).
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