Question

 Find the angle between the two lines `2x = 3y = -z and 6x =-y = -4z`

Answer 1

2x = 3y = -z 

`x/3 = y/2 = Z/-6`
and 6x = -y = -4z

`cos theta = |(a_1a_2 + b_1b_2 + c_1c_2)/sqrt(a_1^2 + b_   )|`

               = `|(3(4)+2(-24)+ (-6)-6)/(sqrt((3^2+ 2^2+6^2)) .sqrt((4^2 +24^2 + 6^2 )))|`

             `=|(12-48+36)/(sqrt(9+4+36).sqrt(16+576+36)) |`

              = 0
 `theta =90°`
Angle between the two lines 2x = 3y = -z and 6x  = -y =-74z is 90°.