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If the point $[x_{1} + t (x_{2} - x_{1}), y_{1} + t (y_{2} - y_{1}), z_{1} + t (z_{2} - z_{1})]$ divides the line segment joining and $(x_{2}, y_{2}, z_{2})$ internally then

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t<0

0<t<1

t>1

t=1

answer is B.

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Detailed Solution

$\frac{x_{1} - x}{x - x_{2}} = \frac{(x_{1} - x_{2}) t}{(x_{1} - x_{2}) (1 - t)}$
Internally $\frac{t}{1 - t} > 0 \Rightarrow t (1 - t) > 0$
$\Rightarrow (t - 0) (t - 1) < 0 \Rightarrow 0 < t < 1$

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