Going over vector fields and i was wondering how they got the solution to the following problem (#1):
There is no x or y, so how would i be able to plot points to sketch the field?
solution:
thanks.
It may be helpful to remember that a vector field assigns a vector to each point in $\displaystyle \mathbb{R}^2$
So in your case what it is saying is
$\displaystyle \vec{F}(x,y)=\frac{1}{2}(\vec{i}+\vec{j})$ this is telling you that the x component of the vector is $\displaystyle x=\frac{1}{2}$ and the y component is $\displaystyle y =\frac{1}{2}$
So for any point in space (the vector field does not depend of x or y) the vector at that point is $\displaystyle \frac{1}{2}\vec{i}+\frac{1}{2}\vec{j}$