In which ratio does the Y Z plane divide the line joining the points \left(\right. - 2 , 4 , 7 \left.\right) and \left(\right. 3 ,

Engineering

Mathematics

Line of Greatest Slope

Question

In which ratio does the

Y Z

plane divide the line joining the points

(- 2, 4, 7)

and

(3, - 5, 8)

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Let

A B

be the line segment joining the points

A (- 2, 4, 7)

and

B (3, - 5, 8)

Let

Y Z

-plane divide the line

A B

P (x, y, z)

in ratio

k : 1

Therefore,

Coordinate of

P = (\frac{3 k - 2}{k + 1}, \frac{- 5 k + 4}{k + 1}, \frac{8 k + 7}{k + 1})

Since

P

lie on the

Y Z

-plane, its

x

-coordinate will be

0

∴ \frac{3 k - 2}{k + 1} = 0

\Rightarrow k = \frac{2}{3}

\Rightarrow k : 1 = 2 : 3

Hence the

Y Z

-plane divides the line

A B

in ratio

2 : 3

Please subscribe our Youtube channel to unlock this solution.