Find the angle between the following pair of lines: (i) `(x-2)/2=(y-1)/5=(z+3)/(-3)`and `(x+2)/(-1)=(y-4)/8=(z-5)/4`(ii) `x/2=y/2=z/1`and `(x-5)/4=(y-2)/1=(z-3)/8`

Explanation

To find the angle between the given pairs of lines, we will use the formula for the cosine of the angle \( \theta \) between two lines represented in vector form:

\[ \cos \theta = \frac{a_1 a_2 + b_1 b_2 + c_1 c_2}{\sqrt{a_1^2 + b_1^2 + c_1^2} \cdot \sqrt{a_2^2 + b_2^2 + c_2^2}} \]

where \( (a_1, b_1, c_1) \) and \( (a_2, b_2, c_2) \) are the direction ratios of the two lines.

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