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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 x22\frac { x - 2 } { 2 } =

= z66\frac { z - 6 } { - 6 } is –

A

6

B

7

C

72\frac { 7 } { 2 }

D

83\frac { 8 } { 3 }

Answer

7

Explanation

Solution

Given plane is x – y – z = 9 … (1)

Given line AB is x22\frac { x - 2 } { 2 } = y+23\frac { y + 2 } { 3 } = z66\frac { z - 6 } { - 6 } … (2)

Equation of line passing through (1, 0, –3) and parallel to

= = z66\frac { z - 6 } { - 6 } is:

= = z+36\frac { z + 3 } { - 6 } = 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.