The coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio 2:1 is ____________________(a) (3, 4, 5)(b) (5, 4, 3)(c) (5, 3, 4)(d) (4, 5, 3)I have been asked this question in a job interview.I would like to ask this question from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 11

The coordinates of a point dividing the line segment joining (1, 2, 3)

1.	The coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio 2:1 is ____________________(a) (3, 4, 5)(b) (5, 4, 3)(c) (5, 3, 4)(d) (4, 5, 3)I have been asked this question in a job interview.I would like to ask this question from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 11
Answer» The correct choice is (a) (3, 4, 5) For explanation I would say: The COORDINATES of a point dividing the line SEGMENT joining (x1, Y1, z1) and (x2, y2, z2) INTERNALLY in the ratio m : n is \((\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n})\). So, the coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio 2:1 is \((\frac{24+11}{2+1},\frac{25+12}{2+1},\frac{26+13}{2+1})\) = (3, 4, 5).

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