the vector v with initial point (0, 0) is shown below. write v in the form v = ai + bj, where a and b are…

the vector v with initial point (0, 0) is shown below. write v in the form v = ai + bj, where a and b are integers.

the vector v with initial point (0, 0) is shown below. write v in the form v = ai + bj, where a and b are integers.

Answer

Explanation:

Step1: Determine the change in x - coordinate

The initial point is $(0,0)$ and the terminal - point of the vector can be observed from the graph. The x - coordinate of the terminal point is $- 6$ and the y - coordinate of the terminal point is $2$. The change in x, $a$, is the x - coordinate of the terminal point minus the x - coordinate of the initial point. So $a=-6 - 0=-6$.

Step2: Determine the change in y - coordinate

The change in y, $b$, is the y - coordinate of the terminal point minus the y - coordinate of the initial point. So $b = 2-0 = 2$.

Answer:

$\mathbf{v}=-6\mathbf{i}+2\mathbf{j}$