1. J

    Interpreting Scalar Product (formula in equations), Please help!

    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. SenatorArmstrong

    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. SenatorArmstrong

    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. B

    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. P


    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. R

    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. S

    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. B

    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. P

    Determine a scalar equation

    Determine a scalar equation for the plane that passes through the point (2,0,−1) and is perpendicular to the line of intersection of the planes 2x + y – 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. K

    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. P

    Sound - scalar or vector?.

    Is Sound a scalar or vector?. Thanks & Regards, Prashant S Akerkar
  12. H

    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. B

    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. B

    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. M

    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. M

    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. Ben Hunto

    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. Z

    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. A

    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. S

    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....