The VECTOR is a light all terrain tactical vehicle in service with the Royal Netherlands Army and Navy. The vehicle is produced by Dutch defense contractor Defenture.
This question has been bugging me for quite a while, That what do we mean by direction of angular velocity or torque. As we know that the direction of angular velocity or torque even is determined by right hand thumb rule, and it come out to be perpendicular to the rotational plane. So my...
This post parallels a post I made in electrical engineering regarding the S plane. I thought I would post an equivalent in basic physics.
So, given a graph of velocity vs time we have on the vertical axis meters/sec and the hormonal axis just meters. Given a plot of V vs t we know the area...
In the S plane we have a real component, usually called sigma, and the imaginary component, jw, in radians/sec. The real component is sometimes called nepers per second, with nepers being dimensionless. However, if we draw a vector in the s-plane, say s - s1, in polar form, what are the units...
Some axially symmetric star has two independent KVFs, ##T## and ##\Phi##. We don't know the expressions for these at all points -- the only thing we know is that as ##r^2 + z^2 \rightarrow \infty##, that ##T \rightarrow \partial/\partial t## and ##\Phi \rightarrow \partial/\partial \phi##. The...
This is the general suggested approach given in a textbook.
My question is why can I not directly write it in vector form?
E1 vector + E2 vector =0 should be valid no?
Why are they choosing to write E1 mag + E2 mag=0
Then find a vector form
Then convert the magnitude equation into a vector...
The problem and solution is,
However, I am confused how they get ##\vec a = (1, 2)## (I convert from column vector to coordinate form of vector). I got ##\vec a = (a_1, a_2) = (a_1, 2a_1) = a_1(1, 2)## however, why did they eliminate the constant ##a_1##?
Thanks for any help!
O level question; i used similarity would appreciate an easier approach for 2 marks.
The ms solution (approach) is not clear to me. Here it is;
My approach; using similarity
Any insight welcome its a 2 mark question- cannot seem to find easier way though i suspect reflection.
Hello,
I have watched a really good Youtube video on linear algebra by Dr. Trefor Bazett and it made me think about a question...
()
Personal Review
A basis in 2D space is formed by any two independent vectors that are not collinear geometrically. Any vector in the 2D space can then be...
In Dirac's GTR. Sec. 12 (p. 22), he wants to show the equivalence of:
(a) Vanishing of the curvature tensor ##R^\beta_{\sigma\nu\rho}=0##; or equivalently, the equality of mixed second covariant derivatives ##A_{\nu:\sigma:\rho}=A_{\nu:\rho:\sigma}##.
(b) Path independence of parallel transport...
I first calculated the time using y = (viy)(t) + 0.5gt^2 where y is the vertical displacement which is 0 for the ball landing back on the ground, viy is the initial vertical velocity ie 16.55m/s and g = -9.8m/s}^2. I get 2 values for t, t=0 and t= 3.377s. Then using the equation x = (vix)(t) =...
Going through this ( Revision) A salways your insights are quite helpful.
I would like to go through all these questions; i will start with (5),
##\left( \dfrac {x} {y} \right)## = ##\left( \dfrac {10 \cos 40^0} {10 \sin 40^0} \right)## + ##\left( \dfrac {4 \cos 150^0} {4\sin 150^0}...
Ok. My problem is what angle to choose when adding vector. Statement does not tell me which one is the "first" force vector. So, when using the law of sine formula I get two results.
First, using cosine to get the magnitude:
$$\vec c = \sqrt{a^2 + b^2 +2ab\cos\theta},$$
$$\vec c = \sqrt{15^2 +...
How do you derive the position vector in a general local basis?
For example, in spherical coordinates, it's ##\vec r =r \hat {\mathbf e_r}##, not an expression that involves that involves the vectors ## {\hat {\mathbf e_{\theta}}}## and ## \hat {{\mathbf e_{\phi}}}##. But how would you show this?
Can a vector subspace have the same dimension as the space it is part of?
If so, can such a subspace have a Cartesian equation?
if so, can you give an example.
Thanks in advance;
All I know is that e subscript r must be a vector cos the book says so, but what does it mean, is it, a konstant in vector form? I'm confused by it (page one, chapter one spacetime and geometry by SeanCaroll)
Help is appreciated
Edit. Is vector r describing the curvature that takes place ?
I am extremely confused with how to represent vectors that do not start at the origin in spherical coordinate system. If they did start at the origin, the vector to any point is simply ##r\pmb{\hat{r}}##; however, what if it does not start at the origin as in the question above? One thing I can...
What am I trying to do for ##\vec V=\vec a \phi## :
##R.H.S= \oint \vec V \cdot d \vec \lambda=\oint \vec a \phi \cdot d \vec \lambda=\vec a \cdot \oint \phi d \vec \lambda ##
##L.H.S= \iint_S \vec \nabla \times \vec V \cdot \vec d \sigma=\iint_S \vec \nabla \times (\vec a \phi) \cdot \vec d...
So I do know that there does exist a generalization of the cross product (the exterior product), but this question does not concern that (and I would prefer it not )
I know that the cross product (that Theodore Frankel, for example, calls "the most toxic operation in math") works in 3D only...
Hi,
I have made the following ContourPlot in mathematica and now I wanted to ##\vec{r}_1= \left(\begin{array}{c} -1 \\ 1 \end{array}\right)##, ##\vec{r}_2= \left(\begin{array}{c} 0 \\ \sqrt{2} \end{array}\right)## and ##\vec{r}_3= \left(\begin{array}{c} 1 \\ 1 \end{array}\right)## insert the...
I am not sure why latex is not rendering, but here is the question.
The answer is ##\frac{a^2}{8}## and for the love of my life, I don't know how. Can you please help me with this?
So i found the magnitude which is
(-1)^2 + (-2)^2 = P^2 =
Sqrt(5)
Then I used the inverse tan function to find the angle (direction)
theta = arctan (-2/-1) = 63.8 degrees
Im confused with my 63.8 degrees since the angle in the graph looks greater than 63.4 degrees
I subtracted 180 by 63.8 and...
So for 1 I know it's Yes you can, but I don't understand what uniquely means here so I can't say if it's uniquely or not.
for 2 I've never seen a 2-D vector broken into 3 reference axies so I guess No?
What really confuse me is the answers which goes 1-C and 4-A
I don't get what is the difference when I am asked to re-solve components and find projections to axes other than the Y and X
I know that the parallelogram works for the first one and the dot product for the second but what's the diffrence!
The problem is actually a solved example
My attention is focused in understanding the displacement vector diagram as it has to deal with question (iv).
I have no problem understanding the velocity vector sketch below:
As you can see ND is the velocity of the river current due East and NE is...
This homework statement comes from a research paper that was published in SPIE Optical Engineering. The integral $$\int\int_{-\infty}^{\infty}drdr'W(\vec{r})W(\vec{r'}) \vec{r} \cdot \vec{r'}=0$$ is an assumtion that is made via the following statement from the paper : "Since...
I am looking at this now; pretty straightforward as long as you are conversant with the formula: anyway i think there is a mistake on highlighted i.e
Ought to be
##-\dfrac{15}{37}(i+6j)##
just need a confirmation as at times i may miss to see something. If indeed its a mistake then its time...
Suppose a stationary reference frame, any other reference frame will have a clock that advances at t'= t/gand is moving away at velocity v. g is the relativistic factor.
we can write:
C d t' = Cdt/g and
d x = v dt
this can be written
(Cdt',Cdx)=(C/g,C v) dt ;
since 1/g2+ v2 =...
Given that c = 3i + 4j and d = i - 2j, find u if uc + d is parallel to i + 3j,
this is the question
in the solution,
it says that we have to multiply the 3 with the i
i do know that this is the ”method“ to do this question but I’d like a bit of explanatio.
I don’t understand why the 3 is...
An airplane has an air velocity of 500 km/h [N 30 E] and encounters a wind from [S 75 W] at 180 km/h, find the ground velocity. Make sure you draw a big, labelled diagram.
Please help! I’m understand the calculations that need to be done (cosine law then sine law for the angle) but I’m a little...
At first I thought that this force vector ## \vec F = 3 \hat x + 2 \hat y ## is a function of ## x ## and ## y ##, which is to say that its magnitude and direction vary with the x and y positions, but this is not so, right? It's just a force with a constant magnitude and direction.
And I can...
Good Morning
(And apologies if this is not the right forum -- it is not a homework problem.)
On the one hand, a vector is an arrow and a tail: it has magnitude and direction. It is used to describe direction, forces, acceleration, etc.
However, there are more mathematical definitions: a...
(a)
##\vec G=24xy\hat a_x+12(x^2+2)\hat a_y+18z^2\hat a_z## @ ##P(1,2-1)##
##\vec G=24(1)(2)\hat a_x+12(1^2+2)\hat a_y+18(-1)^2\hat a_z##
##\vec G=48\hat a_x+36\hat a_y+18\hat a_z##
(b)
I am not sure how to get this part started. Could someone point me in the right direction?
We were taught that in cylindrical coodrinates, the position vector can be expressed as
And then we can write the line element by differentiating to get
.
We can then use this to do a line integral with a vector field along any path. And this seems to be what is done on all questions I've...
For (b) of this problem,
The solution is,
However, I am confused why the two parallel vectors are ##(\frac{2}{\sqrt{13}}, \frac{3}{\sqrt{13}})## and ## (-\frac{2}{\sqrt{13}}, -\frac{3}{\sqrt{13}}) ## should it not be ##(2,3)## and ##(-2,-3)##. Do somebody please know why they wrote that?
Also...
I'm sorry, this touches so many areas, I just didn't know which pigeon hole to put it in, so I dropped it here in General.
Simple summary.
I have two physics equations. The problem I'm trying to solve is a follower is chasing a target that is moving at a fixed velocity. The follower is going...
Dear Everybody,
I am having trouble with last part of this question.
I believe the answer is no. But I have to proof the general case. Here is my work for the problem:
Suppose that we have two distinct norms on the same vector space ##X## over complex numbers. Then there exists no ##K## in...
[mentor's note - moved from one of the homework help forums]
Homework Statement:: It's a question.
Relevant Equations:: Vector calculus.
Is it true to say that in one dimension I can show vector quantities using ±number instead of a vector?
± can show possible directions in one dimension and...
Hi. I hope everyone is well. I'm just an old person struggling to make sense of something I've read and I would be very grateful for some assistance. This is one of my first posts and I'm not sure all the LaTeX encoding is working, sorry. Your help pages suggested I add as much detail as...
Determine the amount and type (tensile or compressive) of the spring force so that the resulting force is a vertical force. Also get the resultant force.
i find 60N (compressive)
and resultant forces is 10800
is that correct?
Member CB of the vise shown exerts on block B a force P directed along line CB. Knowing that P must have a (1237) N horizontal component, determine (a) the magnitude of the force P, (b) its vertical component
i don't get it what the "N horizontal component"