Mean Value Theorem

Step 1: Use the condition for collinearity of vectors.
For two vectors to be collinear, one must be a scalar multiple of the other. That is, for vectors and , we have:
Step 2: Set up the equation.
The given vectors are: Equating and , we get the system of equations:
Step 3: Solve for .
From the third equation: Substitute into the second equation: Thus, the value of is: