Question

Given that P (3, 2, –4), Q (5, 4, –6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR.

Answer 1

The given points are P=( 3,2,−4 ) , Q=( 5,4,−6 ) and R=( 9,8,−10 ) .

Let the ratio in which Q divides PR be k:1 .

According to section formula,

Q( x,y,z )=( m x 2 +n x 1 m+n , m y 2 +n y 1 m+n , m z 2 +n z 1 m+n )

Therefore, considering the x coordinate,

5= k⋅9+1⋅3 k+1 5k+5=9k+3 9k−5k=5−3 4k=2 k= 1 2

Therefore, the point Q=( 5,4,−6 ) divides PR in the ratio 1:2 .