To find the vector that is perpendicular to and , and makes an obtuse angle with , we proceed as follows:

Step 1: Perpendicularity Condition
must be perpendicular to and . The cross product gives a vector that is perpendicular to both and :

Calculating the determinant:

Thus, must be of the form .
Step 2: Obtuse Angle with
makes an obtuse angle with , so :

Step 3: Magnitude Condition
Given :

Since ,

Step 4: Calculating

──────────────────────────────────────────────────────────────────────────────────────────