Question

The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line `x/2 = y/3 = (z - 1)/(-6)` is ______.

Options

• 1

• 2

• 4

• None of these

Answer 1

The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line `x/2 = y/3 = (z - 1)/(-6)` is 1.

Explanation:

Equation of the line through (1, –2, 3) parallel to the line `x/2 = y/3 = (z - 1)/(-6)` is 

`(x - 1)/2 = (y + 2)/3 = (z - 3)/(-6)` = r (say)  ...(i)

Then, any point on equation (i) is (2r + 1, 3r – 2, –6r + 3).

If this point lies on the plane x – y + z = 5, then (2r + 1) – (3r – 2) + (–6r + 3) = 5

`\implies` –7r + 6 = 5

`\implies` r = `1/7`

Since, the point is `(9/7, -11/7, 15/7)`

Distance between (1, –2, 3) and `(9/7, -11/7, 15/7)`

= `sqrt((4/49 + 9/49 + 36/49))`

= `sqrt((49/49))`

= 1