If

L₁: (x−a)/2 = (y−2)/3 = (z−b)/6

and

L₂: (x−b)/3 = (y−7)/6 = (z−1)/3

intersect in the xy-plane, find |a+b|.

Since the lines intersect in the xy-plane:

z = 0

Using z-coordinate equations:

0 = b + 6λ

0 = 1 + 3μ

μ = −1/3

Substituting in x and y equations and solving simultaneously gives:

a + b = 15

Final Answer

15