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Question
Find the angle between the following pairs of lines:
`(x-2)/2 = (y-1)/5 = (z+3)/(-3)` and `(x+2)/(-1) = (y-4)/8 = (z -5)/4`
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Solution
The direction ratios of the given lines are 2, 5, −3 and −1, 8, and 4, respectively.
If the angle between the given lines is θ, then
cos θ = `(a_1a_2 + b_1b_2 + c_1c_2)/(sqrt(a_1^2 + b_1^2 + c_1^2). sqrt(a_2^2 + b_2^2 + c_2^2))`
= `((2) (-1) + (5) (8) + (-3) (4))/(sqrt(2^2 + 5^2 +(-3)^2). sqrt((-1)^2 + 8^2 + 4^2))`
= `(-2 + 40 - 12)/(sqrt38. sqrt81)`
= `26/(9sqrt38)`
⇒ θ = `cos^-1 26/(9sqrt38)`
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