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

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Given,

two points A(–2, 4, 7) and B(3, –5, 8)

Let Y-Z plane divides AB in \lambda:1

So, According to the section formula, the point which divides AB in \lambda:1 is 

\left ( \frac{3\lambda-2}{\lambda+1},\frac{-5\lambda +4}{\lambda+1},\frac{8\lambda +7}{\lambda+1} \right )

Since this point is in YZ plane, x coordinate of this point will be zero.

So,

\frac{3\lambda-2}{\lambda+1}=0

{3\lambda-2}=0

\lambda = \frac{2}{3}

Hence YZ plane divides Line segment AB in a ratio 2:3.

Posted by

Pankaj Sanodiya

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