# scalar

Hello all, I have recently been advancing my knowledge of mathematics by working through worksheets online. However, I am stumped at these particular questions, and have no clue where to begin and answer! Any chance of any answers? Answers would be appreciated as I can work through the steps...
2. ### Scalar Fields vs Vector Fields

I am trying to figure out which expressions are a scalar field and which ones are a vector field. For (a) I figured that we are taking a radial component into our function and taking the gradient. Which I believe would result in a scalar value thus making this a scalar field. For (b)...
3. ### Switching scalar field to polar coordinates

I am trying to take this scalar field $\phi$(r)=$\exp[x^2+y^2] * sin(x^2 - y^2)$ And switch to polar coordinates. But every time I do so I get trig functions sandwiched together. The $x^2 + y^2$ in the exp is simple as it's just r^2. However, the $x^2 - y^2$ in the sin function becomes a...
4. ### Vectors: where k is a scalar quantity

Hello, I'd really appreciate some help with this particular question on vectors. The website is not offering answers. The question is: In the diagram above (not drawn to scale) X is the point on AB such that AX:XB=9:4. The position vector of A is 3a and the position vector of B is...
5. ### Equilibrium

What is the SI unit of Equilibrium? Is Equilibrium scalar or vector quantity? Can we define laws of Equilibrium similar to law of inertia or Newton's laws of motion? Thanks & Regards, Prashant S Akerkar
6. ### Scalar Line Integral

Hello all, I'm trying to understand the scalar line integral, enough so that I should be able to do it without the formula. But I got kind of confused at the end of the first image (attached). I was thinking that adding up the lengths of all of the tangent vectors would give the total length of...
7. ### combination of scalar product and vector product equation

// all leters should have vector symbols above them. (a x b) . (c x d) + (a x c) . (d x b) + (a x d) . (b x c) = 0 I really do not know how to start solving it ... please, help me!
8. ### Affine transform between infinite dimensional quantized space and 1d scalar space

e^sum(log(integerA)+log(integerB)...) = integerA*integerB*... log(integerA)+log(integerB)... = log(integerA*integerB*...) Every unique bag (set that allows duplicates) of primes multiplies to (and factors from) a unique positive integer. Like in Godel Numbering, if dimensions are numbered...
9. ### Determine a scalar equation

Determine a scalar equation for the plane that passes through the point (2,0,âˆ’1) and is perpendicular to the line of intersection of the planes 2x + y â€“ z + 5 = 0 and x + y + 2z + 7 = 0. I know that the line of intersection is in both planes, so its direction vector must be perpendicular to...
10. ### Scalar triple

I need to prove a variety of vector product identities.ex)the scalar triple product.. It is straight forward but very tedious to prove them by direct calculation showing left side equal right..are there some tools a can use to show these identities in a less tedious way?
11. ### Sound - scalar or vector?.

Is Sound a scalar or vector?. Thanks & Regards, Prashant S Akerkar
12. ### Scalar Equation of a Plane

Determine a scalar equation for the plane through the points M(1, 2, 3) and N(3 ,2, -1) that is perpendicular to the N plane with equation 3x + 2y + 6z + 1 = 0. I get that Ax + By + Cz + D = 0 is needed but im doing e learning and am really not sure how to apply it to solve this question
13. ### Scalar product

Hey guys! :) I hope you all had a great weekend! I have a question concerning a math problem I am solving.. we have : hebergeur d images the question is to find : BI . BC (vector) done AC . ED (vector) done Show that CA . CD (vector)= -54 without finding the value of...
14. ### Need help with Closure under scalar multiplication

I am having difficulty proving this axiom. My last response from my instructor was this: Support for law 6 is not sufficient. The requirements are to solve and explain each step of the axiom. This is what I have so far, I hope someone can help me fix my errors. Closure under scalar...
15. ### Derivative of a scalar function w.r.t. a matrix

I need to calculate derivative of the following function with respect to matrix X: f(X)=||diag(X^TX)||_2^2 where diag() returns diagonal elements of a matrix into a vector. How can I calculate \frac {\partial f(X)} {\partial X}? Thanks in advance!
16. ### how to tell if something is closed under addition and scalar multipliction f

I am having serious trouble trying to figure out this whole, "being closed under addition and scalar multiplication" Our example is Let W={[a,b,c]:a+b=4c;b=2c} I need to figure out if it is closed under addition and scalar multiplication, I am not sure how to do this though.. do I...
17. ### Scalar Products, Derivatives and Unit Vectors

In my text there is a section on Conservation of Energy of a Point Mass. Starting with Newton's Second Law as: F = ma = m dv/dt = mg Gravitational field close to Earth is approximately -gz, where z is the unit vector on the z-axis. m dv/dt = -mgz Then take the scalar (dot) product of both...
18. ### Scalar coordinate for a length of a vector

Task 2.31 |[-3,4]| The answer is 5 the book says. But i get = |[-3,4]| = -3^2 + 4^2 = -9 + 16 = 7 sqrt = 2.65 To get 5 i need to have 9 + 16 = 25 sqrt = 5 My question is how does -9 turn too + 9. ?
19. ### Scalar triple product and abstract vector space

Dear all, Can anyone please explain how the linear combination of non-coplanar and non-orthogonal coordinate axes representing a point x as shown below in the attachment is derived. Please use the reference text attached in this post to explain to me as i will find it a bit relevant. I want to...
20. ### linear Operator// scalar produkt

Hi, Let V be a komplex Vector space, and T a linear Operator on V i have to Show: <T(u),u>=0 \forall u \in V \Rightarrow T=0 In course we have just discussed Hermitian adjoint Hope someone could give me a tip for the proof....