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Question
If the point (x1+t(x2−x1),y1+t(y2−y1),z1+t(z2−z1)) divides the line segment joining (x1,y1,z1) and (x2,y2,z2) internally in the ratio t1−t, then the possible values of t lies in the interval:
If the point (x1+t(x2−x1),y1+t(y2−y1),z1+t(z2−z1)) divides the line segment joining (x1,y1,z1) and (x2,y2,z2) internally in the ratio t1−t, then the possible values of t lies in the interval:
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Solution
The correct option is B 0<t<1
(x1+t(x2−x1),y1+t(y2−y1),z1+t(z2−z1)) is the point which divides the line joining (x1,y1,z1) and (x2,y2,z2) in the ration t:1−t
Since, the point divides internally
∴ ratio must be positive
t1−t>0 and t>0
Thus, 0<t<1
(x1+t(x2−x1),y1+t(y2−y1),z1+t(z2−z1)) is the point which divides the line joining (x1,y1,z1) and (x2,y2,z2) in the ration t:1−t
Since, the point divides internally
∴ ratio must be positive
t1−t>0 and t>0
Thus, 0<t<1
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