\( \vec{a} \) and \( \vec{b} \) are two unit vectors that are mutua...

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\( \vec{a} \) and \( \vec{b} \) are two unit vectors that are mutually perpendicular. A unit vector that is equally inclined
P to \( \vec{a}, \vec{b} \) and \( \vec{a} \times \vec{b} \) is
(1) \( \frac{1}{\sqrt{2}}(\vec{a}+\vec{b}+\vec{a} \times \vec{b}) \)
(2) \( \frac{1}{2}(\vec{a} \times \vec{b}+\vec{a}+\vec{b}) \)
(3) \( \frac{1}{\sqrt{3}}(\vec{a}+\vec{b}+\vec{a} \times \vec{b}) \)
(4) \( \frac{1}{3}(\vec{a}+\vec{b}+\vec{a} \times \vec{b}) \)
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