Question

The coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) externally in the ratio 2:1 is ____________________

(a) (4, 5, 6)

(b) (6, 8, 9)

(c) (7, 8, 9)

(d) (8, 6, 4)

I got this question in an international level competition.

I'd like to ask this question from Three Dimensional Geometry topic in chapter Three Dimensional Geometry of Mathematics – Class 11

Answer 1

Right choice is (c) (7, 8, 9)

For explanation: The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) externally 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) externally in the ratio 2:1 is \((\frac{2*4-1*1}{2-1},\frac{2*5-1*2}{2-1},\frac{2*6-1*3}{2-1})\) = (7, 8, 9).