Let \( \vec{x}, \vec{y} \) and \( \vec{z} \) be three vectors each ...

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Let \( \vec{x}, \vec{y} \) and \( \vec{z} \) be three vectors each of magnitude \( \sqrt{2} \)
(a) \( \overrightarrow{\mathrm{b}}=(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{z}})(\overrightarrow{\mathrm{z}}-\overrightarrow{\mathrm{x}}) \)
P and the angle between each pair of them is \( \frac{\pi}{3} \). If \( \vec{a} \) is a
(b) \( \overrightarrow{\mathrm{a}}=(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{y}})(\overrightarrow{\mathrm{y}}-\overrightarrow{\mathrm{z}}) \)
W nonzero vector perpendicular to \( \vec{x} \) and \( \vec{y} \times \vec{z} \) and \( \vec{b} \) is a
(c) \( \vec{a} \cdot \vec{b}=-(\vec{a} \cdot \vec{y})(\vec{b} \cdot \vec{z}) \) nonzero vector perpendicular to \( \vec{y} \) and \( \vec{z} \times \vec{x} \), then
[JEE Advanced-2014]
(d) \( \overrightarrow{\mathrm{a}}=(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{y}})(\overrightarrow{\mathrm{z}}-\overrightarrow{\mathrm{y}}) \)
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