To solve the problem and find the value of [tex]\(2ab \cos C\)[/tex] given the law of cosines, we start with the law's formula:
[tex]\[
a^2 + b^2 - 2ab \cos C = c^2
\][/tex]
The goal is to isolate and determine the value of [tex]\(2ab \cos C\)[/tex].
First, let's rearrange the formula to solve for [tex]\(2ab \cos C\)[/tex]:
[tex]\[
a^2 + b^2 - c^2 = 2ab \cos C
\][/tex]
This equation shows the relationship between the sides of the triangle and the cosine of angle [tex]\(C\)[/tex]. The term we want to find, [tex]\(2ab \cos C\)[/tex], is on the right side of this equation.
From the numerical results:
[tex]\[
2ab \cos C = -7
\][/tex]
Thus, the value of [tex]\(2ab \cos C\)[/tex] is [tex]\(\boxed{-7}\)[/tex].
