Given two orthogonal vectors \( \vec{A} \) and \( \vec{B} \) each o...

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Given two orthogonal vectors \( \vec{A} \) and \( \vec{B} \) each of length unity. Let \( \vec{P} \) be the vector satisfying the equation \( \vec{P} \times \vec{B}=\vec{A}-\vec{P} \). Then
Which of the following statements is false?
(1) vectors \( \vec{P}, \vec{A} \) and \( \vec{P} \times \vec{B} \) are linearly dependent.
(2) vectors \( \vec{P}, \vec{B} \) and \( \vec{P} \times \vec{B} \) are linearly independent.
(3) \( \vec{P} \) is orthogonal to \( \vec{B} \) and has length \( 1 / \sqrt{2} \)
(4) none of the above.
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