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Question: The co-ordinates of the point which divides the join of the points (2, –1, 3) and (4, 3, 1) in the r...

The co-ordinates of the point which divides the join of the points (2, –1, 3) and (4, 3, 1) in the ratio 3 : 4 internally are given by

A

27,207,107\frac { 2 } { 7 } , \frac { 20 } { 7 } , \frac { 10 } { 7 }

B

157,207,37\frac { 15 } { 7 } , \frac { 20 } { 7 } , \frac { 3 } { 7 }

C

107,157,27\frac { 10 } { 7 } , \frac { 15 } { 7 } , \frac { 2 } { 7 }

D

207,57,157\frac { 20 } { 7 } , \frac { 5 } { 7 } , \frac { 15 } { 7 }

Answer

207,57,157\frac { 20 } { 7 } , \frac { 5 } { 7 } , \frac { 15 } { 7 }

Explanation

Solution

From x=m1x2+m2x1m1+m2,y=m1y2+m2y1m1+m2x = \frac { m _ { 1 } x _ { 2 } + m _ { 2 } x _ { 1 } } { m _ { 1 } + m _ { 2 } } , y = \frac { m _ { 1 } y _ { 2 } + m _ { 2 } y _ { 1 } } { m _ { 1 } + m _ { 2 } },

z=m1z2+m2z1m1+m2z = \frac { m _ { 1 } z _ { 2 } + m _ { 2 } z _ { 1 } } { m _ { 1 } + m _ { 2 } } ; x=207,y=57,z=157x = \frac { 20 } { 7 } , y = \frac { 5 } { 7 } , z = \frac { 15 } { 7 }