Show that the line through the points (1, -1, 2) and (3, 4,-2) is perpendicular to the through the points (0, 3,2) and (3, 5, 6).

Explanation

Given points are `A(-1,-1,2, B(3,4,-2), C(0,3,2)` and `D(3,4,6)`
Directi on ratios of line AB
`= [3-1,4-1(-1),-2-2]`
`=(2,4+1,-4)=(2,5,-4)`
Direction ratios of line `CD = (3-0,5-3,6-2)` or `(3,2,4)`
`:. a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2) = 2xx3+5xx2+(-4)xx4`
`= 6+10-16=0`
Therefore, lines AB and CD are mutually perpendicular.