Linear Equations In Two Variables

The problem requires us to determine the range of such that the angle between vectors and is obtuse. An obtuse angle implies that the dot product of these vectors is negative.

First, calculate the dot product:

For the angle to be obtuse, the dot product should be negative:

Factor out :

Based on the inequality, there are two critical points where the expression changes its sign: and . By testing intervals around these points:

• In the interval ,
• In the interval ,
• In the interval ,

Thus, the condition for an obtuse angle is satisfied for .