Dot product Definition and 382 Threads

Homework Statement See the image http://tinypic.com/r/33z6vz5/7 Homework Equations The rules of dot product multiplication. The Attempt at a Solution I've determined that 2 of the solutions are valid, while two of the choices are invalid. I thought C and D looked correct, making A...

Homework Statement Under what conditions are the following true? a) |\mathbf{a}\cdot \mathbf{b}| =|\mathbf{a}||\mathbf{b}| b) (\mathbf{a} + \mathbf{b}) \cdot (\mathbf{a} - \mathbf{b}) = |\mathbf{a}|^2 - |\mathbf{b}|^2 Homework Equations None. The Attempt at a Solution a) I...

Homework Statement Let A(theta)x = b for each theta in S. Calculate, (x dot b)/(|x||b|) A = [cos(theta) -sin(theta) sin(theta) cos(theta)] How is this related to theta? Recall that x dot y and |x| are the standard dot-product and magnitude, respectively, from vector-calculus...

A person pulls a wagon up an incline that makes an angled of 30 deg with the horizontal with a force on the handle of 30 pounds which makes an angel of 30 deg with the incline find the work done in pulling the wagon 100 ft 20cos30 will be a force along the surface of the incline and since...

if A = 2i^+6k^ B=6i^+5j^ find A.B if A.B=0 then what do u conclude from it? one more question if A = 6i^+9k^ and B=-4i^+4j then find A+B,A-B,A.B

S(\vec{q})= \int_0^r exp(i\vec{q}\cdot\vec{x})4\pi x^2 \ dx How would one approach this integral? I tried to "ignore" the dot product and proceeded with exp(i\vec{q}\cdot \vec{x})=exp(iqx) and got a wrong answer.

Homework Statement n. Let r1 and r2 be differentiable 3-space vector-valued functions. Directly from the definition of dot product, and the definition of derivative of vector- valued functions in terms of components, prove that d/dt (r1(t) • r2(t)) = r′1(t) • r2(t) + r1(t) • r′2(t). Homework...

If X is an N vector, is it 1) possible for X*X to be negative? 2) if x*x=0, what is X. I am having trouble writing the proper proof. for 1 I stated that it is impossible for X*X to be negative bc if x is positive, X*X is positive and if x is negative, -X*-X is still positive. for 2 I...

hi, i don't really understand what's the difference between vector product and dot product in matrix form. for example (1 2) X (1 2) (3 4) (3 4) = ? so when i take rows multiply by columns, to get a 2x2 matrix, i am doing vector product? so what then is dot producT? lastly...

i'm reviewing for a test and I can't remember how to do the cross product of (2A)x(3B) or how to find the angle theta when given components. or dot product: 2A . 3B

Homework Statement Given triangle ABC with vertices A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6)..is ABC a Right triangle Homework Equations The Attempt at a Solution I took the dot product of vertices A(4, 1, 7).B(-2, 1, 1), and it gives 0..but however I am a little confused, as...

Homework Statement Expand and simplify: (2\vec{a} + 3\vec{b}) .(5\vec{a} - \vec{b} Homework Equations The Attempt at a Solution I tried expanding it, but was a little confused, and would really appreciate any help..would it be (2\vec{a})(\vec{a}) = 2 \vec{a}2? Thanks..

Homework Statement what is the dot product of G{\bullet}A where A = \left(\frac{a_3}{l}-\frac{{a_1}}{h}\right) and G = 2{\pi}h{\frac{{a_2}}x{{a_3}}}{{a_1}{\bullet}{{a_2}}x{{a_3}}} Homework Equations The Attempt at a Solution The answer is zero and I've got the worked solution...

Homework Statement This isn't so much a problem of calculation, so much as it is I need to know if i did it right, you'll see what I mean. vectors v=(2,0,2), u=(-1,1,0), w=(0,-1,1) Computer the quantities that make sense (a period denotes the dot product, x denotes cross product)...

By evaluating the dot product, find the values of the scalar s for which the two vectors b=X+sY and c=X-sY are orthogonal also explain your answers with a sketch: my working (X,sY).(X,-sY) has to equal 0 for them to be orthogonal x.x = 1 since they are unit vectors...

Homework Statement Show that the dot product of vectors a and b is equal to 1/4|a+b|^2 - 1/4|a-b|^2 Homework Equations a dot b = |a||b|cos(theta) a dot b = a1b1 + a2b2 + ... The Attempt at a Solution I've tried using the combination of the cosine law and those two above dot...

I am reading through David Widder's Advanced Calculus and he abbreviates a determinant as: \left( \begin{array}{cccc} r_{1} \ s_{1} \ t_{1}\\ r_{2} \ s_{2} \ t_{2}\\ r_{3} \ s_{3} \ t_{3}\\ \end{array} \right) And refers to it by (rst). He then states...

Homework Statement My book states as follows: --- If u and v have the coordinate vectors X and Y respectively in a given orthonormal basis, and the symmetric, linear map \Gamma has the matrix A in the same basis, then \Gamma(u) and \Gamma(v) have the coordinates AX and AY, respectively. This...

OK, this has been bugging me for a while. Why is it that \mathbf{v} \cdot \frac{d \mathbf{v}}{d t} = 1/2 v^2 where regular v is just the magnitude of bold v or more specifically where does the 1/2 coefficient turn up.

In what follows, I'll use bold for 4-vectors and an arrow over a letter to denote a 3-vector. I'll use a dot both for the Minkowski dot product and the Euclidean one, and multiplication of real numbers; the meaning in each case should be clear from the symbols on either side. \vec{v} and \vec{a}...

Why not make dot(u,v)=transpose(u)v rather than transpose(v)u?

Homework Statement I have came up with an example to illustrate my question. There is a rod, which can turn around p1. p1p2 = (-1+j) m p1p3 = (-3 + 3j) m p1p4 = (1 - j ) m F1 = (1+3j) N F3 = (-1 - 2j ) N F4 = unknown, orthogonal to the rod compute F2_n, orthogonal component of F2 to the...

Homework Statement Suppose that A is an n x n matrix such that A(Transpose)A=I. Let x be any vector in R^n. Show that llAxll=llxll; that is, multiplication of x by A produces a vector Ax having the same length as x. Homework Equations Sqrt(x(transpose)x)=llxll The Attempt at a...

This question has a few parts. r = i + 2j + 3k s = 2i - 2j - 5k t = i - 3j - k Evaluate: a)(r.t)s - (s.t)r b)(r x s) x t. deduce that (r.t)s - (s.t)r = (r x s) x t can you prove this relative true for any three vectors a)(r.t)s - (s.t)r (r.t)s well I don't know...

Hi, Can someone tell me if: -E dotted with ( A + B ) is equal to -E.A -E.B where E, A and B are all vectors What I mean is, does the minus sign appear on the E.B bit as well? Also, is \int \frac{d}{dt} (A) dV equal to: \frac{d}{dt} \int (A) dV Thank you

In the equation v^2 = u^2 + 2aS , What kind of products are v^2 , u^2 , and aS ? Cross product or dot product?

Homework Statement Prove that, if \vec{r}(t) is a differentiable vector valued function, then so is ||\vec{r}(t)||, and \vec{r}(t) \bullet \vec{r'}(t) = ||\vec{r}(t)|| ||\vec{r}(t)||'Homework Equations I know how to do a dot product, but what bothers me is the fact that the question involves...

Homework Statement Let \vec{A}, \vec{B}, and \vec{C} be three vectors which are all not in the same plane. Show that \vec{A}{\cdot}(\vec{B}{\times}\vec{C})=\vec{B}{\cdot}(\vec{C}{\times}\vec{A})=\vec{C}{\cdot}(\vec{A}{\times}\vec{B}) Homework Equations Don't know :( The Attempt at...

What does the following mean - \int \textbf{F} \cdot d \textbf{r} I know that its equal to work done. but i have problem in understanding it, what's the varibale. i am familiar with integrate cosxdx. what's is similar to dx in above equation. is it ds. Now how can one get to this from above...

I’ve got a confusion. We know a 1x3 row matrix is a 3-vector i.e. x= [ a b c] Matrix x can be written in vector notation like x= a i + b j + c k where i, j, k are unit vectors along x,y & z axes. For dot product of x.x = a2 + b2 + c2 when x= a i + b j + c k But according to...

I am having problems with this questions my physics teacher gave us. Since he doesn't explain things well, I do not know how he got an answer of 66. Can you please explain to me how to get this answer? THX. For the following three vectors, what is C*(A X 3B) (the "*" is suppose to be a dot)...

Hi, Im having trouble understanding something in one of my Dynamics lectures. The lecturer said that: dr/dt dotted with d2r/dt2 (where r is a vector) equals: (1/2)(d/dt(dr/dt dotted with dr/dt))... I just can't get this result. I know it has something to do with the product rule...

Question Let vectors \vec{A} =(2,1,-4), \vec{B}=(-3,0,1), \vec{C}=(-1,-1,2). What is the angle (in radians) \theta_{AB} between \vec{A} and \vec{B}?Important equations \vec{A} \cdot \vec{B} = \vert \vec{A} \vert \,\vert \vec{B}\vert \cos(\theta), where \theta is the angle between \vec{A} and...

Describe the surface defined by the equation: (a) \vec{r}\cdot \hat{x}= 2, where \vec{r}=x\hat{x}+y\hat{y}+z\hat{z}; (b) \left \| \vec{r} \times \hat{x}\right \|=2 For the first one, I know that is interpreted as the projection of the r vector onto the x-axis is equal to two...

Greetings. I was thinking about finding the angle between two functions, so I thought it may be elegant to turn them into vector valued functions, and find the dot product at a given variable value where the vectors lie on the same plane and are functions of the same variable. I'm going to go...

Homework Statement I need to find the momentum space function for the ground state of hydrogen (l=m=0, Z=n=1) Homework Equations \phi(\vec{p}) = \frac{1}{(2\pi\hbar)^{3/2}}\int e^{-i(\vec{p}\cdot\vec{r})/\hbar}\psi(\vec{r})d^3\vec{r}...

Homework Statement Which of the following can be computed? 1. A dot B dot C 2. A dot ( B dot C ) 3. A dot ( B + C ) 4. 3 dot A Homework Equations The Attempt at a Solution I believe that 2 and 3 are the only two that can be computed. Can anyone confirm this? Thanks.

The following notation is from the book "Frames and Bases." Let f and g be vectors in R^{n} with the usual dot product <,>. Then, what does the notation \left|\left\langle f,g\right\rangle\right|^{2} mean? Specifically, does it mean \left|\sum^{n}_{i=1}f_{i} g_{i}\right| or does it...

Hi, I'm very ashamed about getting a fully understanding of these vector product concepts. But i did a lot of search and get an idea about them. I read Feynman's lecture on physics and almost completely understand the mathematics behind their properties. In that book feynman proves that cross...

Hi! I am trying to find out where: cos\theta=\frac{a \cdot b}{|a||b|} came from. Here is mine geometrical interpretation of scalar projection: Now, (pr means projection) pr_{\overrightarrow{A}} \overrightarrow{B} = p\overrightarrow{B_0} and...

Hi All, I'm currently studying vector projections and the vector dot product. I ran into a problem on the homework I wasn't quite sure how to tackle... Any suggestions?The problem is stated as follows: Determine ||v+w|| if v and w are unit vectors separated by an angle of \frac{\pi}{6}...

Homework Statement Shown are a mast and a portion of the rigging of a schooner. Members CD and EF lie in the same plane, and CD is of length 7.5 m and forms an angle of 45° with a vertical line drawn through C. Knowing that when \theta = 45° the tension in rope BD is 250N, determine, (a) the...

Homework Statement Vector A and four other vectors that have the same magnitude but differ in orientation. a) Which of those other four vectors have the same dot product with A? b) Which have a negative dot product with A? http://img195.imageshack.us/img195/7079/40191924.th.jpg (Those...

Homework Statement We are studying Electromagnetic Induction right now. I understand the concepts, Faraday's Law and magnetic flux. But I don't understand what my book is doing. Homework Equations Magnetic Flux \phi=\intB∙dA Faraday's Law Emf = - d\phi/dt Emf=Electromotive force \phi=Magnetic...

Homework Statement The cosine of the angle between vector a and vector b is 4/21. Find p. vector a = 6i + 3j - 2k vector b = -2i + pj - 4k Homework Equations (Vector a) . (Vector b) = abcos(theta) (Vector a) . (Vector b) = axbx + ayby + azbz mag(a) = root(ax^2 + ay^2 + az^2) The Attempt at...

How can I show that the binormal vector is orthogonal to the tangent and normal vector. I know i should use the dot product to determine this, however i do i actually go about doing it?

Homework Statement 1. (a) Define carefully the dot and vector products of two vectors a and b. (b) Show, using the dot product, that if c - d and c + d are perpendicular then |c| = |d|. (c) The vectors a = i+2j and b = i - 2j + k form two sides of a triangle. Use vector methods to find...

Homework Statement If theta is the angle between two non-zero vectors A and B, then which of the following angles theta results in A dot B = |A x B|? Homework Equations A dot B = ABcos(theta) A x B = ABsin(theta) The Attempt at a Solution There were two choices in the multiple choice answers...

In some text, I read something like this \vec{S}_i\cdot\vec{S}_j where \vec{S}_i and \vec{S}_j are "vectors" with each components be the pauli matrices S_x, S_y, S_z individularly. My question is: if all components of this kind of vector are a 3x3 matrix, so how do you carry out the dot...

In reading a book on astrodynamics I came across the following statement: \vec{a}\cdot \vec{\dot{a}}=a \dot{a} Where the dotting is the time derivative notation. I put a picture of the original text up, and it's the statement right in the middle...