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

Answer

The direction ratios of the two lines are 3-1, 4+1, -2-2 i.e., 2, 5, -4 and 3-0, 5-3, 6-2 i.e., 3, 2, 4 respectively.
The direction ratios of the line through `(x_1, y_1,z_1)` and `(x_2,y_2,z_2)` are `x_2-x_1, y_2-y_1, z_2-z_1`
`therefore` The sum of products of the direction ratios = `2xx3+5xx2+(-4)xx4 = 6+10-16 = 0 `
Hence, the two lines are perpendicular.