The ratio in which the line joining points \left(\right. 2 , 4 , 5 \left.\right) and \left(\right. 3 , 5 ,

Engineering

Mathematics

Line of Greatest Slope

Question

The ratio in which the line joining points

(2, 4, 5)

and

(3, 5, - 4)

divide YZ -plane is

- 2 : 3

2 : 3

- 3 : 2

3 : 2

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Let the ratio be

λ : 1

The dividing plane is

Y Z

plane.

So, the co-ordinate of

x

after dividing the line

= 0

Now According to internal division rule of line segment

x = \frac{3 \times λ - 1 \times 2}{λ + 1}

\Rightarrow \frac{3 λ - 2}{λ + 1} = 0

\Rightarrow 3 λ - 2 = 0 \Rightarrow λ = \frac{2}{3}

So. Ratio

= 2 : 3

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