Question
Question: The distance of the point (1, 0, –3) from the plane x – y – z = 9 measured parallel to the line \(...
The distance of the point (1, 0, –3) from the plane
x – y – z = 9 measured parallel to the line 2x−2 =
= −6z−6 is –
A
6
B
7
C
27
D
38
Answer
7
Explanation
Solution
Given plane is x – y – z = 9 … (1)
Given line AB is 2x−2 = 3y+2 = −6z−6 … (2)
Equation of line passing through (1, 0, –3) and parallel to
=
= −6z−6 is:
=
= −6z+3 = r … (3)
Co-ordinates of any point on (3) may be given as
p (2r + 1, 3r, –6r – 3)
If P is intersection of (1) and (3) then it must lie on (1) ;
(2r + 1) – (3r) – (–6r – 3) = 9
2r + 1 – 3r + 6r + 3 = 9 Ž r = 1
\ co-ordinate of P are (3, 3, –9)
\ Required distance = distance between (1, 0, –3) and
(3, 3, –9) = 7.