Let the unit vectors \( a \) and \( b \) be perpendicular and the unit vector \( c \) be incline....

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Let the unit vectors \( a \) and \( b \) be perpendicular and the unit vector \( c \) be inclined at an angle \( \theta \) to both \( a \) and
\( \mathrm{P} \)
\( b \). If \( c=\alpha a+\beta b+\gamma(a \times b) \) then
W
(1) \( \alpha=2 \beta \)
(2) \( \gamma^{2}=1+2 \alpha^{2} \)
(3) \( \gamma^{2}=\cos 2 \theta \)
(4) \( \beta^{2}=\frac{1+\cos 2 \theta}{2} \)


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