Question

3. (6 points each) A charged particle is sitting at the point (3, -1, 0). An electric field is exerting a force on this particle with magnitude $F(x, y, z) = 3x - 2y^2 + xyz$. (a) At what instantaneous rate is the magnitude of the force changing when the particle starts moving toward the point (1, 2, -1)? (b) Still assuming the particle is at (3, -1, 0), in which direction would it have to move to make the magnitude of the force increase most rapidly? Give your answer as a unit vector. (c) Suppose the particle is moving along a curve $\vec{r}(t)$. At some time $t = t_0$, the particle has position $\vec{r}(t_0) = (3, -1, 0)$ and velocity $\vec{r}'(t) = (2, 2, 1)$. At what rate is the magnitude of the force on the particle changing with respect to time at $t = t_0$?

          3. (6 points each) A charged particle is sitting at the point (3, -1, 0). An electric field is exerting a force on this particle with magnitude $F(x, y, z) = 3x - 2y^2 + xyz$.
(a) At what instantaneous rate is the magnitude of the force changing when the particle starts moving toward the point (1, 2, -1)?
(b) Still assuming the particle is at (3, -1, 0), in which direction would it have to move to make the magnitude of the force increase most rapidly? Give your answer as a unit vector.
(c) Suppose the particle is moving along a curve $\vec{r}(t)$. At some time $t = t_0$, the particle has position $\vec{r}(t_0) = (3, -1, 0)$ and velocity $\vec{r}'(t) = (2, 2, 1)$. At what rate is the magnitude of the force on the particle changing with respect to time at $t = t_0$?

3. (6 points each) A charged particle is sitting at the point (3, -1, 0). An electric field is exerting a force on this particle with magnitude F(x, y, z) = 3x - 2y^2 + xyz.
(a) At what instantaneous rate is the magnitude of the force changing when the particle starts moving toward the point (1, 2, -1)?
(b) Still assuming the particle is at (3, -1, 0), in which direction would it have to move to make the magnitude of the force increase most rapidly? Give your answer as a unit vector.
(c) Suppose the particle is moving along a curve r⃗(t). At some time t = t0, the particle has position r⃗(t0) = (3, -1, 0) and velocity r⃗'(t) = (2, 2, 1). At what rate is the magnitude of the force on the particle changing with respect to time at t = t0?

Added by Kathleen D.

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