Question

The ratio in which line joining (1, 2, 3) and (4, 5, 6) divide X-Y plane is ________

(a) 2

(b) -2

(c) 1/2

(d) -1/2

The question was asked in final exam.

Enquiry is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 11

Answer 1

Right choice is (d) -1/2

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

Let ratio be k : 1.

So, z-coordinate of the point will be (k*6+1*3)/(k+1).

We know, for X-Y plane, z coordinate is zero.

(6k+1*3)/(k+1) = 0 => k=-1/2