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Question
Find the angle between the following pairs of lines:
`x/y = y/2 = z/1` and `(x-5)/4 = (y-2)/1 = (z - 3)/8`
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Solution
The direction ratios of the given lines are 2, 2, 1 and 4, 1, 8 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) (4) + (2) (1) + (1) (8))/(sqrt(2^2 + 2^2 +1^2). sqrt(4^2 + 1^2 + 8^2))`
= `18/(sqrt9. sqrt81)`
= `18/(3 xx 9)`
= `2/3`
⇒ θ = `cos^-1 (2/3)`
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