Answer:
[tex]a = 2\sqrt{2}[/tex] and [tex]b = 5\sqrt{2}[/tex].
Step-by-step explanation:
The resulting vector is the product of the input and rotation vectors. That is:
[tex]\vec R = \left[\begin{array}{ccc}\cos \theta&\ -\sin \theta\\ \sin \theta&\cos \theta\end{array}\right] \left[\begin{array}{ccc}3\\-7\end{array}\right][/tex]
[tex]\vec R = \left[\begin{array}{ccc}3\cdot \cos \theta + 7 \cdot \sin \theta\\ 3\cdot \sin \theta - 7 \cdot \cos \theta\end{array}\right][/tex]
Now, the resulting vector is determined by evaluating in given angle:
[tex]\theta = \frac{3\pi}{4}[/tex]
[tex]\vec R = \left[\begin{array}{ccc} 2\sqrt{2}\\ 5\sqrt{2}\end{array}\right][/tex]
The resulting vector is [tex](2\sqrt{2} , 5\sqrt{2})[/tex]. Then, [tex]a = 2\sqrt{2}[/tex] and [tex]b = 5\sqrt{2}[/tex].
