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+1 vote
10.9k views
in Three-dimensional geometry by (36.3k points)

Find the distance of the point (1, 0, – 3) from the plane x – y – z = 9 measured parallel to the line (x – 2)/2 = (y + 2)/3 = (6 – z)/6. 

1 Answer

+1 vote
by (33.0k points)
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Best answer

The equation of any line through (1, 0, –3) and parallel to the line (x – 2)/2 = (y + 2)/3 = (6 – z)6 is 

Any point on the line (i) is (2λ + 1, 3λ, – 6 – 3λ)

which is lies in the plane x – y – z = 9. So,

(2λ + 1) – (3λ) – (–6 – 3λ) = 9 

2λ + 7 = 9 

2λ = 2 

λ = 1 

Thus, the point is (3, 3, –9).

Hence, the required distance

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