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Distance between Two Parallel Planes

If Az1, Bz2...

Question

If $A (z_{1}), B (z_{2})$ and $C (z_{3})$ are collinear points, then:

(z_{3} - z_{1}) ({¯ ¯ ¯ z}_{2} - {¯ ¯ ¯ z}_{1}) = ({¯ ¯ ¯ z}_{3} - {¯ ¯ ¯ z}_{1}) (z_{2} - z_{1})

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z_{3} - z_{1} = {¯ ¯ ¯ z}_{2} - {¯ ¯ ¯ z}_{1}

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(z_{3} - z_{1}) ({¯ ¯ ¯ z}_{3} - {¯ ¯ ¯ z}_{1}) = (z_{2} - z_{1}) ({¯ ¯ ¯ z}_{2} - {¯ ¯ ¯ z}_{1})

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Solution

The correct option is D $(z_{3} - z_{1}) ({¯ ¯ ¯ z}_{2} - {¯ ¯ ¯ z}_{1}) = ({¯ ¯ ¯ z}_{3} - {¯ ¯ ¯ z}_{1}) (z_{2} - z_{1})$
If $A (z_{1}), B (z_{2}), C (z_{3})$ are collinear of each other in the plane then the condition is
$\to (z_{3} - z_{1}) ({¯ z}_{2} - {¯ z}_{1}) = ({¯ z}_{3} - {¯ z}_{1}) (z_{2} - z_{1})$

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