- #1
Jhenrique
- 685
- 4
I want find a value M such that given v and u, satisfies the equation v=Mu.
Well, the vector u has a modulus u and a direction α wrt x-axis; the vector v has another modulus v and another direction β wrt x-axis. What is happened is a change of magnitude and direction of the vector u, therefore, M needs scalar the vector u and change its direction, so that:
$$\\ M = \frac{v}{u} \begin{bmatrix}
\;\;\;\cos(\beta-\alpha) & -\sin(\beta-\alpha)\\
+\sin(\beta-\alpha) & \;\;\;\cos(\beta-\alpha)\\
\end{bmatrix}$$
So: $$\\ \frac{\vec{v}}{\vec{u}} = M$$
Well, the vector u has a modulus u and a direction α wrt x-axis; the vector v has another modulus v and another direction β wrt x-axis. What is happened is a change of magnitude and direction of the vector u, therefore, M needs scalar the vector u and change its direction, so that:
$$\\ M = \frac{v}{u} \begin{bmatrix}
\;\;\;\cos(\beta-\alpha) & -\sin(\beta-\alpha)\\
+\sin(\beta-\alpha) & \;\;\;\cos(\beta-\alpha)\\
\end{bmatrix}$$
So: $$\\ \frac{\vec{v}}{\vec{u}} = M$$