Question

The line joining the point (0,5,4) and(1,3,6) neets XY-plane at the point

Answer 1

the line joining the points (0, 5, 4) and (1, 3, 6) meets xy plane.

Solution : direction ratio of line passing through (0, 5, 4) and (1, 3, 6) = (0 - 1, 5 - 3, 4 - 6) = (-1, 2, -2)

Now equation of line will be..

(x - 0)/-1 = (y - 5)/2 = (z - 4)/-2 = k ( let)

In xy plane, z = 0

Then (0 - 4)/-2 = k ⇒ k = 2

So, (x - 0)/-1 = 2 ⇒x = -2

And (y - 5)/2 = 2 ⇒y = 9

Therefore the line joining the point (0, 5, 4) and (1, 3, 6) meets xy plane at the point (-2, 9, 0)

Answer 2

Answer:-

the line joining the points (0, 5, 4) and (1, 3, 6) meets xy plane.

Solution :

direction ratio of line passing through (0, 5, 4) and (1, 3, 6) = (0 - 1, 5 - 3, 4 - 6) = (-1, 2, -2)

Now equation of line will be..

(x - 0)/-1 = (y - 5)/2 = (z - 4)/-2 = k ( let)

In xy plane, z = 0

Then

(0 - 4)/-2 = k ⇒ k = 2

So,

(x - 0)/-1 = 2 ⇒x = -2

And (y - 5)/2 = 2 ⇒y = 9

Therefore the line joining the point (0, 5, 4) and (1, 3, 6) meets xy plane at the point (-2, 9, 0)

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