The linear combination [tex]2\cdot \vec v -3\cdot \vec u[/tex] is equal to [tex]\vec r = -42\cdot i + 14\cdot j[/tex]
The resultant vector is a linear combination of the two vectors described in statement, which is calculated as follows:
[tex]\vec r = -3\cdot (-3,4) + 2\cdot (-5-7,2-0)[/tex]
[tex]\vec r = (9, -12) + (-24, 4)[/tex]
[tex]\vec r = (-15, -8)[/tex]
[tex]\vec r = -15\,\hat{i}-8\,\hat{j}[/tex]
The answer as a linear combination of [tex]\vec u[/tex] and [tex]\vec v[/tex] is [tex]\vec r = -15\,\hat{i}-8\,\hat{j}[/tex].
We kindly invite to check this question on linear combinations: https://brainly.com/question/13350739
