Find the angle between the lines -x-2-2-y-17-z-3-3 and x-2-1-2y-84-z-54- Check if they are parallel or perpendicular-

→ #160; l_1: x 22 = y 17 = z+3 3 l_2 =x+2 1 = y 42 = z 54 cosθ =n⃗_⃗1⃗ n⃗^⃗2⃗ |n⃗_⃗1⃗ | | n⃗_⃗2⃗ | where θ is angle b/w lines #160; ...

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Byju's Answer

Standard XII

Mathematics

Angle between Two Line Segments

Find the angl...

Question

Find the angle between the lines $\frac{- x + 2}{- 2} = \frac{y - 1}{7} = \frac{z + 3}{- 3}$ and $\frac{x + 2}{- 1} = \frac{2 y - 8}{4} = \frac{z - 5}{4}$ . Check if they are parallel or perpendicular.

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Solution

$\to l_{1} : \frac{x - 2}{2} = \frac{y - 1}{7} = \frac{z + 3}{- 3}$
$l_{2} = \frac{x + 2}{- 1} = \frac{y - 4}{2} = \frac{z - 5}{4}$
$cos θ = \frac{_{1} -^{2}}{|_{1} | |_{2} |}$ where $θ$ is angle b/w lines
$_{1}$ is parallel to $l_{1} = (2, 7, - 3)$
$_{2} = (- 1, 2, 4)$
$cos θ = \frac{- 2 + 14 - 12}{\sqrt{n_{1}} . \sqrt{n_{2}}}$ $= 0 \to θ = 90^{\circ}$
$\Rightarrow$ perpendicular

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\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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Find the angle between the following pair of lines

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

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Find the angle between the lines −x+2−2=y−17=z+3−3 and x+2−1=2y−84=z−54. Check if they are parallel or perpendicular.

→l1:x−22=y−17=z+3−3l2=x+2−1=y−42=z−54cosθ=→n1−→n2|→n1||→n2| where θ is angle b/w lines→n1 is parallel to l1=(2,7,−3)→n2=(−1,2,4)cosθ=−2+14−12√n1.√n2 =0→θ=90∘⇒ perpendicular

Find the angle between the lines $\frac{- x + 2}{- 2} = \frac{y - 1}{7} = \frac{z + 3}{- 3}$ and $\frac{x + 2}{- 1} = \frac{2 y - 8}{4} = \frac{z - 5}{4}$ . Check if they are parallel or perpendicular.