Question

Find a vector $V(x,y,z)$ normal to the surface $z=\sqrt{x^2+y^2}+(x^2+y^2)^{3/2}$

score 389 · Answer 1 · 2026-04-17 03:52:47

389

Views

Find a vector $V(x,y,z)$ normal to the surface $z=\sqrt{x^2+y^2}+(x^2+y^2)^{3/2}$

Published on 17 Apr 2026 - 3:52

score 118 · Answer 2 · 2026-04-12 02:08:12

118

Views

show that the equation $r_1+r_2= \text{constant}$ implies the relation $\mathbf{T}\cdot \nabla(r_1+r_2)=0,$

Published on 12 Apr 2026 - 2:08

score 138 · Answer 3 · 2026-04-12 05:51:20

138

Views

Concerning an application of the divergence theorem

Published on 12 Apr 2026 - 5:51

score 38 · Answer 4 · 2026-04-17 06:00:49

If $||\nabla f(x,y)||^2=2$, determine constants $a$ and $b$ such that $a(\frac{\partial g}{\partial u})^2-b(\frac{\partial g}{\partial v})^2=u^2+v^2.$

score 112 · Answer 5 · 2026-04-15 06:14:22

112

Views

If $f(x,y,z)=(r \times A)\cdot (r\times B)$, where $r=(x,y,z)$, show that $\nabla f(x,y,z)=B\times (r\times A)+A\times (r\times B)$.

Published on 15 Apr 2026 - 6:14

score 64 · Answer 6 · 2026-04-16 08:55:47

64

Views

Let $\mathbf{r}=(x,y,z)$,$r=||\mathbf{r}||$. Show the following equation on $B\cdot \nabla (A\cdot \nabla (\frac{1}{r}))$

Published on 16 Apr 2026 - 8:55

score 44 · Answer 7 · 2026-04-13 06:02:49

44

Views

Problems on orthogonality and tangency in 3-space.

Published on 13 Apr 2026 - 6:02

score 259 · Answer 8 · 2026-04-14 08:32:21

259

Views

Showing that a function is the gradient of another function

Published on 14 Apr 2026 - 8:32

score 1k · Answer 9 · 2026-04-16 09:47:21

1k

Views

Explicitly demonstrating Stokes' theorem over a tetrahedron.

Published on 16 Apr 2026 - 9:47

score 4.7k · Answer 10 · 2026-04-09 09:43:14

4.7k

Views

How to determine the maximum rate of increase in temperature

Published on 09 Apr 2026 - 9:43

score 81 · Answer 11 · 2026-04-15 08:20:24

81

Views

Showing that $\nabla (\alpha f) = \alpha \nabla f$ for constant $\alpha$

Published on 15 Apr 2026 - 8:20

score 5.1k · Answer 12 · 2026-04-16 18:59:17

5.1k

Views

Find a unit tangent vector to a curve that is an intersection of two surfaces.

Published on 16 Apr 2026 - 18:59

score 59 · Answer 13 · 2026-04-12 06:17:33

59

Views

Computing partial derivatives using three implicitly defined equations

Published on 12 Apr 2026 - 6:17

score 49 · Answer 14 · 2026-04-17 22:34:45

49

Views

vector triple product does not go from $[\dot{M} \times [H \times M]]+[M \times [H \times \dot{M}]]$ to $2\dot{M}(H,M)$

Published on 17 Apr 2026 - 22:34

score 225 · Answer 15 · 2026-04-12 23:52:34

225

Views

What is nabla scalar (a.u) where a is a scalar field and u a vector field?

Published on 12 Apr 2026 - 23:52

List Question

Find a vector $V(x,y,z)$ normal to the surface $z=\sqrt{x^2+y^2}+(x^2+y^2)^{3/2}$

show that the equation $r_1+r_2= \text{constant}$ implies the relation $\mathbf{T}\cdot \nabla(r_1+r_2)=0,$

Concerning an application of the divergence theorem

If $||\nabla f(x,y)||^2=2$, determine constants $a$ and $b$ such that $a(\frac{\partial g}{\partial u})^2-b(\frac{\partial g}{\partial v})^2=u^2+v^2.$

If $f(x,y,z)=(r \times A)\cdot (r\times B)$, where $r=(x,y,z)$, show that $\nabla f(x,y,z)=B\times (r\times A)+A\times (r\times B)$.

Let $\mathbf{r}=(x,y,z)$,$r=||\mathbf{r}||$. Show the following equation on $B\cdot \nabla (A\cdot \nabla (\frac{1}{r}))$

Problems on orthogonality and tangency in 3-space.

Showing that a function is the gradient of another function

Explicitly demonstrating Stokes' theorem over a tetrahedron.

How to determine the maximum rate of increase in temperature

Showing that $\nabla (\alpha f) = \alpha \nabla f$ for constant $\alpha$

Find a unit tangent vector to a curve that is an intersection of two surfaces.

Computing partial derivatives using three implicitly defined equations

vector triple product does not go from $[\dot{M} \times [H \times M]]+[M \times [H \times \dot{M}]]$ to $2\dot{M}(H,M)$

What is nabla scalar (a.u) where a is a scalar field and u a vector field?

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