Question

Find the points which trisects the line joining (4, 9, 8) and (13, 27, -4).

(a) (7, 4, 15)

(b) (7, 15, 4)

(c) (4, 15, 7)

(d) (4, 7, 15)

I had been asked this question during a job interview.

My doubt is from Three Dimensional Geometry in division Three Dimensional Geometry of Mathematics – Class 11

Answer 1

Right option is (b) (7, 15, 4)

To explain I would say: Points which trisect the line divides it into 2:1 and 1:2.

The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m : n is \((\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n})\).

For 1:2, coordinates of point are \((\frac{1*13+2*4}{1+2},\frac{1*27+2*9}{1+2},\frac{-4+2*8}{1+2})\) = (7, 15, 4)

For 2:1, coordinates of point are \((\frac{2*13+1*4}{1+2},\frac{2*27+1*9}{1+2},\frac{-8+1*8}{1+2})\) = (10, 21, 0)