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

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t<0

t>1

t=1

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detailed solution

Correct option is B

x1+tx2−x1,y1+ty2−y1,z1+z2−z1=tx2+1-tx1,ty2+1-ty,tz2+1-tz1 =tx2+1-tx1t+1-t,ty2+1-ty1t+1-t,tz2+1-tz1t+1-t ⇒the ratio of division is t:1-t Since the division is internal, t1-t>0 ⇒tt-1<0 ⇒0

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If the point x1+tx2−x1,y1+ty2−y1,z1+z2−z1 devides the line segment joining x1,y1,z1) and x2,y2,z2 internally then

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