## Elementary Geometry for College Students (6th Edition)

$l_1: (x,y,z) = (1,-2,5)+n(4,1,-3)$ The direction vector is $(a,b,c) = (4,1,-3)$ $l_2: (x,y,z) = (1,-2,5)+r(-3,6,-2)$ The direction vector is $(d,e,f) = (-3,6,-2)$ We can verify the condition stated in the theorem: $ad+be+cf = (4)(-3)+(1)(6)+(-3)(-2)$ $ad+be+cf = (-12)+(6)+(6)$ $ad+be+cf = 0$ Since the direction vectors of the two lines satisfy the condition stated in the theorem, the two lines are perpendicular.