Lines And Angles

To determine when the lines are perpendicular, we need to find the dot product of their direction vectors and set it equal to zero.

For the first line: Direction vector .

For the second line: Direction vector .

The dot product of and is given by:

Simplifying:

For the lines to be perpendicular, we require:

Simplifying further:

Therefore, the value of that makes the lines perpendicular is: