Dot product Definition and 382 Threads

While taking linear algebra I never really understood where the dot and cross product came from. It seemed that they were just randomly defined. I know that the dot product is an inner product but why is it defined as: \vec v \cdot \vec u = v_1 u_2 + v_2 u_2 ? why not \vec v \cdot \vec u =...

Hi I'm new here and I'm having trouble with this algebra question please help. Sorry if my latex is ugly I'm new to it. I get stuck at the bottom line and I'm not sure how to go further with the question to solve for K #7 - Angle between 2 vectors is \alpha where cos\alpha = \frac{3}{7}. a =...

Ok, this one has really got me... Suppose that u \centerdot (vXw) = 2. Find (a) (uXv) \centerdot w (b) u\centerdot(wXv) (c) v\centerdot(uXw) (d) (uXv)\centerdotv Once I understand the what to do with the information given, I am sure the rest of the problems will fall into place...

I have to present shortly five applications of vector dot product in physics, for example: W=F*s. I am not quite clear about vectors, so could someone advise me.

I'm trying to solve this problem with different approaches. Link is here http://img138.imageshack.us/img138/2268/problem1eb1.th.png the answer is 0i + 0.0927j + 0.0232 k lb* Means DOT Method one: Find the force in scalar components. Then Take the cross product of two position vectors to get...

The question with all the info is: A force F = (6x i + 5y j) N acts on an object as it moves in the x direction from the origin to x = 5.04 m. Find the work (work = integral of F (dot product) dx done on the object by the force. I am confused as to what dx would be in this equation, and how...

Hello. To find the work of a force, I have to perform a dot product between the force and a infinitesimal displacement. If they are in cylindrical coordinates, I can't manage to make the dot product. Please, could you help me? Thank you.

I'm doing a series of questions right now that is basically dealing with the dot and cross products of the basis vectors for cartesian, cylindrical, and spherical coordinate systems. I am stuck on \hat R \cdot \hat r right now. I'll try to explain my work, and the problem I am running into...

-Use the dot product to prove that the quadrilateral with vertices A(-4,1) B(4,5) C(7,-1) and D(-1,-5) is a rectangle. I tried find AB dot BC = 0, but I'm not getting 0. So I'm stumped. Can someone help me out? =/

I have come across something that seems a little strange to me. The derivative of a dot product is something similar to the product rule. I am having difficulties grasping this. Isn't the dot product of two vectors a scalar? And then I always thought of a scalar as a real number and the...

Is there any difference between an inner product and a dot product?

I'm going nuts here and I can't figure this out. I have two complex vectors: A=(1+i)x + (1)y +(i)z B=(4-i)x +(0)y + (2-2i)z If I do the dot product of these on my calculator I get 1 + 7i, however when I do this by hand I keep getting 7 +5i. What am I doing wrong? When figuring this out by...

hi, I'm currently doing a mechanics module at Uni. The thing is, I'm not very sure about rules regarding the vector cross product and dot product. For example, it says in my notes for angular momentum: "Introducing polar coordinates \mathbf{r} = r(cos \Phi \mathbf{i} + sin \Phi...

A force in the xy plane is given by: F= - (b/r3) (x i^ + y j^) where b is a positive constant and r= sqrt(x2 + y2) a) Show that the maginitude of the force varies as the inverse of the square of the distance to the origin and that its direction is antiparallel (opposite) to the radius vector...

Can someone help me with the following question. I've been having trouble with problems of this kind for a while now. Q. If the path u(t) (u is a vector) is differentiable at least three times, simplify: \frac{d}{{dt}}\left[ {\left( {u' \times u''} \right) \bullet \left( {u' - u}...

Hello everyone! I'm confused on what I'm suppose to do here, I think i might got it though but i need to make sure... Here is the problem and my work: http://show.imagehosting.us/show/764032/0/nouser_764/T0_-1_764032.jpg he let r(t) = f(t) i + g(t) j + h(t) k. So if i multiply this by...

hello everyone, i understand the dot product and its properties but i don't get what they want! They say... The dot product of two vectors are perpendicular if a.b = 0. Then any vector in R^3 perpendicular to -5 -6 -3 note: that is a matrix above. can be written in the form...

I am doing a assingment for my classical mechanics class that requires the proof of: The dot product of |A dot B| <= (less than or equeal to) |A| |B| . I did the algebraic proof fine but we are required to do a geometic proof as well. This leaves me with the question what is the geometic...

Hello everyone. I'm trying to show ab = ba. //communative property of dot product This is what I have, is it enough to show this? ab = (ax, ay, az) \dot (bx, by, bz) = axbx + ayby + azbz; a\dotb = (axi + ayj) (bxi + byj); //note: i and j are unit vectors = axbx(i)(i) + ayby(j)(j) +...

I'm a peer leader for a general physics lab and someone asked me to explain what the Dot Product meant conceptually. I told him it was the projection of A onto B multiplied by the magnitude of B. He looked even more confused after that; my questions are: a) Did I explain it correctly...

Hello everyone, does anyone know the proof of the dot products communative property (a)(b) = (b)(a) or any websites that show the dot products communative property? or other properties? Thanks! The book only shows the distributed property.

What is the dot product of a unit vector (e) with a non-unit vector (A)? Is this some sort of identity? Thanks, don_anon25

Well, I've been attempting to learn dot products of vectors and in doing so have come upon some questions. NOTE: a, b, and c are to be regarded as vectors Please regard '*' as the dot for multiplication, too. Question 1: a * b * c When I see this, I am unaware how to approach it...

i need help with the following: note that the big dots represents the dot product 1. suppose that a \bullet b = c \bullet b for all vectors \overrightarrow{b} . show that \overrightarrow{a} = \overrightarrow{c} . i suppose i can't simply divide out the b, right? anyway, i tried...

I have some questions from my geometry and discrete class.. #1 Given a and b unit vectors, a) if the angle between them in 60 degrees, calculate (6a+b)●(a-2b) b) if |a+b|= root(3), determine (2a-5b)●(b+3a) #2 The vectors a=3i-4i-k and b=2i +3j-6k are the daignols of a parallelogram...

i have three vectors: a=4,b=3,c=5 that form a right triangle. vector a is in the positive x direction, vector b is in the positive y direction starting at the tip of a. vector c is the hypotenuse of the triangle with tip at the origin. (see attaced picture .doc file) the questions are...

I'm sorry if this is placed under the wrong section of the forum. But i really need help with a problem. Well, here it is; Find a unit vector that is parallel to the xy-plane and perpendicular to the vector 4i - 3j + k *note* there is a ^ above the ijk.

Let n = (a,b,c) v = (x,y,z) Whatever the dot product of these vectors equal to, let's call d, the vector n is perpendicular to v. Again, I cannot stay calm and ask WHY? If we call n = (a,b); v= (x,y) ==> ax+by= d and the slope of this line is -a/b whereas the slope of the vector n is...

I need some major help with some dot products. I was curious if when getting the dot product, you add the angles of each one to each other. I'll give the problem: theta=(/) Find A*B(dot product) A=8.6i+5j B=9.7i+2.6j So i used the formula my teacher gave me to find the angle, theta...

Hi, I got a simple question, "dot product" have units? I mean, if A=(Ax+Ay+Az)N and B=(Bx+By+Bz)(cm/s) , the units of A.B will be N.(cm/s) Thanks, Cali

The angle between vectors a and b is cos^-1(4/21). Find p if a = [6,3,-2] and b = [-2, p, -4] I did: cos x= 4/21 = a.b/|a||b| The result comes out to be p=8/3 but it only satisfies that a dot b is 4 and not |a||b| = 21...What am I doing wrong?

Here's what I got to prove where '.' is dot. A.B=A.C Then B=C True or false? If true, prove it in general terms, if false, provide a counter-example. Ok, I just need some body to comment on my little proof here, and any guidelines to make it more thorough or whatnot. I know that the dot...