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Question: The point on the line \(\frac{x - 2}{1} = \frac{y + 3}{- 2} = \frac{z + 5}{- 2}\) at a distance of 6...

The point on the line x−21=y+3−2=z+5−2\frac{x - 2}{1} = \frac{y + 3}{- 2} = \frac{z + 5}{- 2} at a distance of 6 from the point (2, –3, – 5) is

A

(3, –5, –3)

B

(4, –7, –9)

C

(0, 2, –1)

D

(–3, 5, 3)

Answer

(0, 2, –1)

Explanation

Solution

Let point is x−21=y+3−2=z+5−2\frac{x - 2}{1} = \frac{y + 3}{- 2} = \frac{z + 5}{- 2} = l

P º (l + 2, –2l – 3, – 2 l – 5)

Q (2, – 3, – 5)

PQ = 6

PQ2 = 36

l + 2 – 2)2 + (–2l – 3 + 3)2 + (2l – 5 +5)2 = 36

9l2 = 36

l2 = 4

l = ± 2

\ from l = 2, P º (4, –7, – 9)

from l = – 2, P º (0, 1, – 1)