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Calculate scalar H number divided by N vector?

Posted 2 months ago
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Hello. I am trying to calculate the vector X as shown in the attached file. But I don't know what commands to use. Can you give me information about this?

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17 Replies

1) N is a Mathematica-Symbol. Look it up in the Help-Section. You shouldn't use N, try vN or so.

2) Your "N" clearly is a vector of dimension 3. But your H is a scalar. Tell me , why should

scalar / vector

an operation that is - at least - not well (if not far from ) defined be a vector? Did you mean N / H ?

Dear Hans,

May I have your email address, please?

Posted 2 months ago

First of all, thank you for your reply. There are vectors N and X such that <N, X> = H. Actually, I'm trying to find the possible values of the X vector. How do I calculate with Mathematica?

I think you mean this

( < vecN , vecX > = H = prod in this code )

vecN = {a, b, c};
vecX = {x1, x2, x3};
scalar = s;
prod = vecN.vecX;     
lsg=Solve[prod == scalar, x1] // Flatten

Then x1 is given as function of x2 and x3. Chose any x2 and x3, calculate x1 and this vector gives your condition.

vecX1 = vecX /. lsg
vecN.vecX1
Posted 2 months ago

These are exactly the codes I'm looking for. Thank you very much for your help.

Posted 2 months ago

Can we divide two vectors? Can we divide two vector quantities? For eg., Pressure( a scalar) equals force (a vector) divided by area (a vector).

No. There is not an operation like vector / vector. By the way, pressure in general is NOT a scalar, but a Tensor:

press = {
   {pxx, pxy, pxz},
   {pyx, pyy, pyz},
   {pzx, pzy, pzz}
   };

and the force experienced by a surface ( given by a vector surf = { sx,sy, sz } is given by

force = press.surf

Often the off-diagonal elements of press are 0 (this is most likely not the case in vsicous fluids) , and if in addition the diagonal elements are equal = p ( an isotropic medium) the force points in the direction of surf. Then you can write

p = Norm[ force ] / Norm[ surf ]  

press = {
   {p, 0, 0},
   {0, p, 0},
   {0, 0, p}
   };
f1 = press.{1, 1, 1}
f2 = press.{2, 3, 4}
Norm[f1]/Norm[{1, 1, 1}]
Norm[f2]/Norm[{2, 3, 4}]
Posted 1 month ago
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Posted 7 days ago

Hello. Although I selected the s value differently in these two files, the same result came out. I couldn't understand the reason. I wonder if the results I get are correct. Where do you think I might have made a mistake?

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Hmmm. These notebooks don't run on my system. What exactly is your question?

Posted 5 days ago

In the equation <N, X> = H, I try to find the vector X. When I change the scalar value "H" here, the result (the vector X) also needs to change. But Mathematica gives the same result. Its stuck on my mind. I wonder where I made a mistake.

Posted 5 days ago

In the equation <N, X> = H, I try to find the vector X. When I change the scalar value "H" here, the result (the vector X) also needs to change. But Mathematica gives the same result. Its stuck on my mind. I wonder where I made a mistake.

Where is your H?

And you write

s = 1/4 ( Abs[ Sin[ b s ] +......

So s appears on both sides of the = sign, I wonder that you don't get error messages.

What about this?

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Posted 3 days ago

Actually, what I want to ask is exactly like this: Here I have changed the sign at the end of the parenthesis (shown in green). I thought the result would also change. But it has not changed. I couldn't understand why.

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Dear Meryem,

I must admit I don't understand exactly what you mean.

As your expressions in fact aren't simple I decided to do some numerical calculations (see notebook). For this purpose I defined an arbitrary function gg to be inserted for g later on.

With several calculations I obtained different solutions for x1 using + or - in H.

Note: the two different solution - vectors differ only in the x1-component by a constant.

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