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If \( z_{1}, z_{2} \) and \( z_{3} \) are vertices of an equilateral triangle whose orthocentre is, the origin, then
(a) \( z_{1}+z_{2}+z_{3}=0 \)
(b) \( \left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right| \)
(c) \( z_{2} z_{3}+z_{3} z_{1}+z_{1} z_{2}=0 \)
(d) \( O z_{1} \) is perpendicular to \( z_{2} z_{3} \).
\( \mathrm{P} \)
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