Find the angle between the lines x-3-3-y-1-5-z-3-4 and x-1-1-y-4-1-z-5-2-

Let (a_1,b_1,c_1) = (3,5,4) and (a_2,b_2,c_2)=(1,1,2) cos θ =a_1a_2+b_1b_2+c_1c_2/√(a^2_1+b^2_1+c^2_1)√(a^2_2+b^2_2+c^2_2) =3+5+8/√(9+25+16)√(1+1+4) =16/√ ...

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

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Solution

$Let (a_{1}, b_{1}, c_{1}) = (3, 5, 4) and (a_{2}, b_{2}, c_{2}) = (1, 1, 2) c o s θ = \frac{a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}} \sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}} = \frac{3 + 5 + 8}{\sqrt{9 + 25 + 16} \sqrt{1 + 1 + 4}} = \frac{16}{\sqrt{50} \sqrt{6}} = \frac{16}{10 \sqrt{3}} \Rightarrow θ = c o s^{- 1} (\frac{8}{5 \sqrt{3}})$

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Find the angle between the following pair of lines

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

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

Q. Angle between the pair of lines

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

and

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

Q. Find the angle between the straight lines

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

and

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

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

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

and

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

(ii)

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

and

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

Q. The angle between the straight lines

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

and

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

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Find the angle between the lines x+33=y−15=z+34 and x+11=y−41=z−52 .

Let(a1,b1,c1)=(3,5,4) and (a2,b2,c2)=(1,1,2)cos θ=a1a2+b1b2+c1c2√a21+b21+c21√a22+b22+c22=3+5+8√9+25+16√1+1+4=16√50√6=1610√3⇒θ=cos−1(85√3)

Find the angle between the lines $\frac{x + 3}{3} = \frac{y - 1}{5} = \frac{z + 3}{4} and \frac{x + 1}{1} = \frac{y - 4}{1} = \frac{z - 5}{2}$ .