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In questions 1-5, let \(\vec{F}(x,y,z) = \langle xz, yz, 0 \rangle\)

1.  Compute div\(\vec{F}(x,y,z)\).

a.  \(2z\)

b.  \(z\)

c.  \(0\)

d.  \(-z\)

e.  \(-2z\)

2.  Compute \(\vec{curl}(\vec{F})\).

a.  \(\langle y, -x, 0\rangle\)

b.  \(\langle y, x, 0\rangle\)

c.  \(\langle -y, -x, 0\rangle\)

d.  \(\langle -y, x, 0\rangle\)

e.  \(\langle 0, 0, 0\rangle\)

3.  If \(\vec{F}\) represents the motion of a fluid, at the point \((1,2,3)\) is the fluid

a.  getting more dense?

b.  getting less dense?

c.  neither getting more nor less dense?

4.  At what points is this fluid neither getting more nor less dense?

a.  All points on the z-axis

b.  Everywhere

c.  Every point above the xy-plane

d.  Every point below the xy-plane

e.  Just on the xy-plane

5.  Are there any points you could anchor a pinwheel where it wouldn't spin at all?

a.  All points on the z-axis

b.  Everywhere

c.  Every point above the xy-plane

d.  Every point below the xy-plane

e.  Just on the xy-plane