Let \( \hat{x}, \hat{y} \) and \( \hat{z} \) and be unit vectors such that \( \hat{x}+\hat{y}+\h...

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Let \( \hat{x}, \hat{y} \) and \( \hat{z} \) and be unit vectors such that \( \hat{x}+\hat{y}+\hat{z}=a \), \( \hat{x} \times(\hat{y} \times \hat{z})=b,(\hat{x} \times \hat{y}) \times \hat{z}=c, a \cdot \hat{x}=\frac{3}{2}, a \cdot \hat{y}=\frac{7}{4} \) and \( |a|=2 \). Find \( x, y \) and \( z \) in terms of \( a, b \) and \( c \).
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