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in Three Dimensional Geometry by (28.2k points)
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The equation of two lines are

  1. Find the dr’s of the given lines. 
  2. Find the angle between the given lines. 
  3. Find the equation of the line passing through (2, 1, 3) and perpendicular to the given lines.

1 Answer

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by (28.9k points)
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Best answer

1. The given lines are

The dr’s of (1) are 2, 2, 3 and dr’s of (2) are -3, 2, 5.

2. The angle between (1) and (2) is given by

3. Let a, b, c be the dr’s of the line perpendicular to lines (1) and (2).

∴ 2a + 2b + 3c = 0, -3a + 2b + 5c = 0

Solving by the rule of cross-multiplication, we get

∴ dr’s of the required line are 4, -19, 10 and the line passes through (2, 1, 3).

∴ Equation of the required line is

\(\frac{x-2}{4}= \frac{y-1}{-19}= \frac{z-3}{10}.\)

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