# Find the Angle Between the Two Lines 2 X = 3 Y = − Z and 6 X = − Y = − 4 Z - Mathematics

Sum

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

#### Solution

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°.

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