Find the acute angle between lines (x - 1)/1 = (y - 2)/-1 = (z - 3)/2 and (x - 1)/1 = (y - 2)/1 = (z - 3)/1.

Question

Find the acute angle between lines \(\frac{x - 1}{1}=\frac{y - 2}{-1}=\frac{z - 3}{2}\) and \(\frac{x - 1}{1}=\frac{y - 2}{1}=\frac{z - 3}{1}.\)

(x - 1)/1 = (y - 2)/-1 = (z - 3)/2 and (x - 1)/1 = (y - 2)/1 = (z - 3)/1

Answer 1

(x - 1)/1 = (y - 2)/-1 = (z - 3)/2 

and (x - 1)/1 = (y - 2)/1 = (z - 3)/1

Let \(\overline{a}\) and \(\overline{b}\) be the vectors in the direction of the lines

\(\frac{x - 1}{1}=\frac{y - 2}{-1}=\frac{z - 3}{2}\) and \(\frac{x - 1}{1}=\frac{y - 2}{1}=\frac{z - 3}{1}\) respectively.

If θ is the angle between the lines, then