Let \( A \) and \( B \) be two distinct point denoting the complex number \( \alpha \) and \( \b...

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Let \( A \) and \( B \) be two distinct point denoting the complex number \( \alpha \) and \( \beta \) respectively. \( A \) complex number \( z \) lies between \( A \) and \( B \) where \( z \neq \alpha, z \neq \beta \). Which of the following relation(s) hold good?
(a) \( |\alpha-z|+|z-\beta|=|\alpha-\beta| \)
(b) \( \exists \) a positive real number \( t \) such that \( z=(1-t) \alpha+t \beta \)
(c) \( \left|\begin{array}{ll}z-\alpha & \bar{z}-\bar{\alpha} \\ \beta-\alpha & \bar{\beta}-\bar{\alpha}\end{array}\right|=0 \)
(d) \( \left|\begin{array}{lll}z & \bar{z} & 1 \\ \alpha & \bar{\alpha} & 1 \\ \beta & \bar{\beta} & 1\end{array}\right|=0 \)
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