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Parallel Lines and Intersecting Lines

Find the angl...

Question

Find the angle between the following pairs of lines:

(i)

(ii)

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Solution

Let and be the vectors parallel to the pair of lines, , respectively.

and

The angle, Q, between the given pair of lines is given by the relation,

(ii) Let be the vectors parallel to the given pair of lines, and , respectively.

If Q is the angle between the given pair of lines, then

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Q. Find the angle between the following pair of lines:
(i)

\frac{x - 2}{2} = \frac{y - 1}{5} = \frac{z + 3}{- 3}

\frac{x + 2}{- 1} = \frac{y - 4}{8} = \frac{z - 5}{4}

\frac{x}{2} = \frac{y}{2} = \frac{z}{1}

\frac{x - 5}{4} = \frac{y - 2}{1} = \frac{z - 3}{8}

Find the angle between the following pair of lines

$\frac{x - 2}{2} = \frac{y - 1}{5} = \frac{z + 3}{- 3} a n d \frac{x + 2}{- 1} = \frac{y - 4}{8} = \frac{z - 5}{4}$

$\frac{x}{2} = \frac{y}{2} = \frac{z}{1} a n d \frac{z - 5}{4} = \frac{y - 2}{1} = \frac{z - 3}{8}$

Q. Angle between the pair of lines

\frac{x - 2}{1} = \frac{y - 1}{5} = \frac{z + 3}{- 3}

\frac{x + 1}{- 1} = \frac{y - 4}{8} = \frac{z - 5}{4}

Q. Find the angle between the following pair of lines

\frac{x}{2} = \frac{y}{2} = \frac{z}{1} a n d \frac{z - 5}{4} = \frac{y - 2}{1} = \frac{z - 3}{8}

Q. Find the angle between the following pairs of lines:
(i)

\frac{x + 4}{3} = \frac{y - 1}{5} = \frac{z + 3}{4} and \frac{x + 1}{1} = \frac{y - 4}{1} = \frac{z - 5}{2}

\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{- 3} and \frac{x + 3}{- 1} = \frac{y - 5}{8} = \frac{z - 1}{4}

\frac{5 - x}{- 2} = \frac{y + 3}{1} = \frac{1 - z}{3} and \frac{x}{3} = \frac{1 - y}{- 2} = \frac{z + 5}{- 1}

\frac{x - 2}{3} = \frac{y + 3}{- 2}, z = 5 and \frac{x + 1}{1} = \frac{2 y - 3}{3} = \frac{z - 5}{2}

\frac{x - 5}{1} = \frac{2 y + 6}{- 2} = \frac{z - 3}{1} and \frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 6}{5}

\frac{- x + 2}{- 2} = \frac{y - 1}{7} = \frac{z + 3}{- 3} and \frac{x + 2}{- 1} = \frac{2 y - 8}{4} = \frac{z - 5}{4}

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