All Questions
6
questions
0
votes
1
answer
93
views
Which law of dot product should I know in order to understand this equivalence: $ \bf v.dv =$ $d$ $(\bf v.v)$?
The context is an exercise in which it is asked to derive a well known formula regarding work :
$W=\int_{t1}^{t2} \bf F.d\bf r$ $= \frac{1}{2} mv_2^2 - \frac{1}{2} mv_1^2$
where $v_1$ and $v_2$ denote ...
- 158
0
votes
2
answers
72
views
Calculating $\nabla\left(\nabla \cdot \boldsymbol{r}_{0} e^{i\boldsymbol{k} \cdot \boldsymbol{r}}\right)$
In a longer derivation I ran into the following quantity:
$$
\nabla\left[\nabla\cdot\left(%
{\bf r}_{0}\,{\rm e}^{{\rm i}{\bf k} \cdot {\bf r}}\,\right)
\right]
$$
( i.e., the gradient of the ...
- 53
1
vote
0
answers
77
views
Confusion with gradient and divergence of vector fields and scalar fields
In a proof, my teacher used the following assumption for an approximation:
$$
|\nabla n(\boldsymbol{r}, t)| \ll\left|\nabla \partial_{t} \boldsymbol{\tilde{r}}(\boldsymbol{r}, t)\right|
$$
where $n$ ...
- 853
0
votes
2
answers
267
views
Find the normal vectors of the two angle-bisecting planes.
Compute the coordinate equation of the angle bisectors of the planes E
and F.
$E: x + 4y + 8z + 50 = 0 $ and $F: 3x + 4y + 12z + 82 = 0$
Proceed as follows:
a) Find the normal ...
- 51
-2
votes
2
answers
859
views
Determine point of intersection or find the value of $z$ [closed]
Let $L_1$ be the line passing through the points $Q_1=(4, −2, −4)$ and $Q_2=(5, −1, −5)$ and let $L_2$ be the line passing through the point $P_1=(−13, −12, 6)$ with direction vector $\underline{d}=[6,...
- 251
2
votes
0
answers
156
views
Vector equation of line containing point and perpendicular to plane [duplicate]
How would one find the vector equation of the line that contains the point (x0, y0, z0) and is perpendicular to the plane Ax + By + Cz = D?
- 321