The ratio in which the join of \left(\right. 1 , - 2 , 4 \left.\right) and \left(\right. 4 , 2 , - 1 \left.\right) divided by the X Y plane is

Engineering

Mathematics

Line of Greatest Slope

Question

The ratio in which the join of

(1, - 2, 4)

and

(4, 2, - 1)

divided by the

X Y

plane is

1 : 3

3 : 1

4 : 1

1 : 4

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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

(\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 + 4 n = 0

or,

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

or,

m : n = 4 : 1

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