Question

Angle between the lines (x-1)/2=(y+1)/-1=z/-2 and (x+1)/-1=(y-3)/-2=(z-1)/2

Answer 1

Answer:

63.6° (approx)

Hope this helps.

Step-by-step explanation:

A vector in the direction of the first line is (from the denominators):

u = ( 2, -1, -2 ).

A vector in the direction of the second line is:

v = ( -1, -2, 2 ).

The magnitudes of these vectors are:

|u| = √( 2² + (-1)² + (-2)² ) = √( 4 + 1 + 4 ) = √9 = 3

|v| = √( (-1)² + (-2)² + 2² ) = √( 1 + 4 + 4 ) = √9 = 3

The dot product of these vectors is:

|u| |v| cos θ = u . v = (2)(-1) + (-1)(-2) + (-2)(2) = -2 + 2 - 4 = -4.

=>  cos θ = -4 / (|u| |v|) = -4/9

=>  θ ≈ 116.4°

Or, preferring the acute angle between the lines, we can say the angle is the supplement:

≈ 180° - 116.4° = 63.6°