The ratio in which the join of (1, –2,4) and (4, 2,

Engineering

Mathematics

theorem in space

Section Formulae and Centres of a Triangle

Distance from a Plane

Question

The ratio in which the join of (1, –2,4) and (4, 2, –1) divided by the XY plane is

1 : 4

1 : 3

4 : 1

3 : 1

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

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 P be the point where the line joining the given two points (1, –2, 4) and (4, 2, –1) intersects the X – Y plane in m : n ratio. We are to find m : n.

Now the co-ordinate of the point P be

(\frac{4 m + n}{m + n}, \frac{2 m - 2 n}{m + n}, \frac{- m + 4 n}{m + n})

As the point P lies on the X – Y plane

\frac{- m + 4 n}{m + n} = 0

or, –m + 4n = 0

or,

\frac{m}{n} = \frac{4}{1}

or, m : n = 4 : 1