Question

Find the terminal point of the vector that is equivalent to $\mathbf{u}=(1,2)$ and whose initial point is $A(1,1)$.

Answer 1

The terminal point of a vector is the point that the vector points to or ends at. To find the terminal point of a vector, we need to add the vector to the initial point of the vector.

In this case, the initial point of the vector is given as $A(1,1)$, and the vector is given as $\mathbf{u} = (1,2)$. To find the terminal point, we simply add the coordinates of the vector to the coordinates of the initial point, like this:

$$\begin{aligned} A + \mathbf{u} &= (1,1) + (1,2) \ &= (1 + 1, 1 + 2) \ &= (2,3) \end{aligned}$$

Therefore, the terminal point of the vector is $\boxed{(2,3)}$.