Question

The direction ratios of the line segment joining \(P(x_1,y_1,z_1)\) and \(Q(x_2,y_2,z_2)\) is given by _______, ____________ and __________

(a) \(x_2+x_1,y_2+y_1,z_2+z_1\)

(b) \(x_2-x_1,y_2+y_1,z_2-z_1\)

(c) \(x_2-x_1,y_2-y_1,z_2-z_1\)

(d) \(x_2+x_1,y_2-y_1,z_2+z_1\)

The question was asked in semester exam.

This interesting question is from Direction Cosines and Direction Ratios of a Line topic in section Three Dimensional Geometry of Mathematics – Class 12

Answer 1

Correct choice is (c) \(x_2-x_1,y_2-y_1,z_2-z_1\)

Easiest explanation: Let a.,b,c be the direction ratios of the line segment PQ.

Then, the direction ratios of the line segment joining \(P(x_1,y_1,z_1)\) and \(Q(x_2,y_2,z_2)\) is given by

\(a=x_2-x_1\)

\(b=y_2-y_1\)

\(c=z_2-z_1\)