Question

Short answer

The vector field \(F\) matches with the plot II.

Step-by-step solution

Given Information.

The given vector field is \(F(x,y,z){\rm{ }} = {\rm{ }}xi + yj + zk\).

Select the matching plot and give reason.

In the given vector field, if we keep x and y constant, then the vector increases in magnitude with increase in z and it points in positive z-direction if z is positive and in negative z-direction if z is negative.

If we keep y and z constant, then the vector increases in magnitude with increase in x and it points in positive x-direction if x is positive and in negative x-direction if x is negative.

If we keep x and z constant, then the vector increases in magnitude with increase in y and it points in positive y-direction if y is positive and in negative y-direction if y is negative.

Therefore, the vector field \(F\) matches with the plot II.