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).

Solution:

Given that
The points and .
Let’s consider be the line joining the points, and , and be the line through the points , and .
So now,
Direction ratios, of are

In the similar way,
The direction ratios, of are

Therefore, and will be perpendicular to each other, if

As a result, and are perpendicular to each other.