Describing a Vector Field in Space
Describe the vector field \(\mathbf{F}=\mathbf{F}(x,y,z)=y\bf{j}\) by drawing some of the vectors \(\bf{F}.\)
| \(( x,y,z)\) | \(( 0,0,0) \) | \(( 0,1,1)\) | \(( 0,1,2)\) | \(( 0,-1,-1)\) | \((1,-1,0) \) | \(( 1,3,1) \) | \(( 1,-2,-1))\) |
|---|---|---|---|---|---|---|---|
| \(\bf{F}( x,y,z) \) | \(\bf{0}\) | \(\bf{j}\) | \(\bf{j}\) | \(-\bf{j}\) | \(-\bf{j}\) | \(3\bf{j}\) | \(-2\bf{j}\) |
Each vector in the vector field \(\bf{F}\) is parallel to the \(y\)-axis. The magnitude of the vector equals \(\left\vert y\right\vert \) and is proportional to the distance of the vector from the \(xz\)-plane. See Figure 4.