Question

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

Answer 1

The given points are A=( −2,4,7 ) and B=( 3,−5,8 ) .

Let Q=( x,y,z ) be the point in YZ-plane which divides AB in the ratio m:n .

Since Q lies in the YZ-plane, the value of x is 0 .

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,

0= m⋅3+n⋅( −2 ) m+n 0=3m−2n 3m=2n m n = 2 3

Therefore, the ratio in which the YZ-plane divides the line segment formed by joining the points A=( −2,4,7 ) and B=( 3,−5,8 ) is 2:3 .