Parallelogram Definition and 123 Threads

Homework Statement Determine resultanat force of vectors P (40N) and Q (60N). P is 20 degrees from reference plane and Q is 45 degrees from reference plane. Homework Equations When using the parallelogram rule, should you always start with the lowest angle vector? (like in the bottom...

[b]1. The area of a parallelogram is 60 square units. A segment is drawn from one vertex to the midpoint of an opposite side. The diagonal is drawn between the other two other vertices. Find the area of the four regions formed. Homework Equations [b]3. I found that two of the...

Homework Statement Incl. diagrams: http://i.imgur.com/w6Exj.png Homework Equations Just vector addition (?)The Attempt at a Solution a.) ED = x(BD) ED = x(a+b) b) EQ = y(AQ) = y(b-0.5a) From the smaller triangle: ED = EQ + QD ED = [y(b-0.5a)] + (0.5a) I am not sure if this is what part b is...

Homework Statement Find the area of the paralellogram with vertices P1, P2, P3, and P4. *Not all pairs of vertices will give rise to a side. P1 = (1, 2, -1) P2 = (4, 2, -3) P3 = (6, -5, 2) P4 = (9, -5, 0) Homework Equations ||U X V || is the area of the parallelogram having U≠0 and...

Homework Statement Evlute the surface integral Homework Equations f(x,y,z)=x+y+z where sigma is the parallelogram with parametric equations x=u+v, y=u-v and z=1+2u+v where 0 <=u<=2 and 0<=v<=1. The Attempt at a Solution I have no idea how to tackle this. Any suggestions?

Homework Statement Apply the formula for the distance between two points to prove the well-known theorem: In a parallelogram the sum of the squares of the sides is equal to the sum of the squares of the diagonals. Homework Equations It gave a hint saying to put one of the...

1. I'll illustrate the question, I've been having a lot of troubles with it, the image is in the attachements. 2. I've tried it many times, with different methods but keep getting different answers. Really need help with it. Most recently tried by splitting it into two triangles then working...

Hi there! My question involves the area of a parallelogram. Now, I know how to prove the commonly used formula (b*h) very easily, however, there is a formula given on Wikipedia as an alternative that states...Given two sides B and C with angle (theta), B*C*sin(theta)=Area of a parallelogram. Now...

In Kolmogorov and Fomin's Real Analysis book, pg. 161, they make the following claim: For any vectors f,g,h in a real Hilbert space, we have \|f + g + h\|^2 + \|f - h - g\|^2 = 2\|f - h\|^2 + 2\|g\|^2. They attempt to justify this using the parallelogram law: \|x + y\|^2 + \|x -...

Homework Statement P is the point where the diagonals of the parallelogram abcd intersect one another let \alpha = AB and \beta = AD and let s and t be scalars such that AP = sAC and BP = tBD use vector algebra to show that s(\alpha + \beta) = AP = \alpha + t(\beta - \alpha)The Attempt at...

(2 dimensions.) Given 2 forces acting on an object (not modeled as particle), you can project their lines so that you can find a point of intersection - X. On this point of intersection exists no moment caused by the 2 forces since the line action makes 0 degrees with the forces. It follows that...

Consider the parallelogram with adjacent sides OP; OQ where P is the point (x1; x2); Q is the point (y1; y2) and O is the origin.What does this ||x + y||^{2}+ ||x - y||^{2} = 2(||x||^{2} + ||y||^2)say about a parallelogram in the plane? I know ||x + y|| & ||x -y|| represent the diagonals...

In school, we've been using the parallelogram method to calculate the resultant force of 2 forces. I've noticed the teacher using his calculator to give the answer, so I think there must be a formula to calculate Resultant force. Can someone tell me the formula please ?

This is a (fairly basic) lemma without proof I saw in a research paper. Wasn't sure how to classify it exactly, but decided it's closest to vector (and linear) algebra. It goes like this, consider a quadrilateral in the plane with vertices A, B, C, D in clockwise order. It is given that...

Homework Statement If three corners of a parallelogram are (1,1), (4,2), and (1,3), what are all the possible fourth corners? Homework Equations The Attempt at a Solution The only possible fourth corner is (4,4) if the other 3 points are set. The solution says (4,0) and...

Homework Statement The diagonals of quadrilateral ABCD bisect each other. Use vectors to prove that ABCD is a parallelogram. The Attempt at a Solution let O = point of intersection AO = AD + DO DO = 1/2DB AO = AD + 1/2 DB AO = AB + BO BO = -1/2DB AO = AB - 1/2DB 2AO = AD...

Homework Statement Sketch the parallelogram spanned by <2,1,0> and <-3,1,0> in the xy-plane, and compute its area. Homework Equations The Attempt at a Solution I have already computed the area, so I don't need help with that part. I do need help sketching the parallelogram...

Homework Statement Let z_1, z_2, z_3 and z_4 be te position vectors of the vertices of quadrilateral AMCD. Prove that ABCD is a parallelogram if and only if z_1-z_2-z_3+z_4=0. Homework Equations The Attempt at a Solution The solution obviously uses the fact that collinear vectors of equal...

Homework Statement Find the area of the parallelogram defined by the vectors v = {1 1 3 1} w = {-2 -1 2 2} Homework Equations Area = v dot w * sin(theta) theta = cos^-1(v dot w / |v|*|w|) The Attempt at a Solution Solved General Solution: Area of a parallelogram for non-R^3 vectors = v dot...

Perhaps Tensor Calculus holds the answer; but I just can't justify the time for studying that as I know nothing of it. The end objective is to calculate the mass moment of inertia of the yellow solid parallelepiped about rectangular axes through its centre of mass as in the diagram here...

Homework Statement Parallelogram in 3d with vectors. Points: A(2,-1,4); B(1,0,-1); C(1,2,3); D(2,1,8) I need the interior angle at B in degrees. Homework Equations cos(theta) = (Vector1 dot product vector2) / (magnitude of v1 * magnitude of v2) The Attempt at a Solution I...

Homework Statement ABCD is a parallelogram with <BAD=60. Lines AM and BM bisect Angles BAD and ABC respectively. Perimeter of ABCD is 6. Find lengths of the sides of triangle ABM. [PLAIN]http://img709.imageshack.us/img709/2440/stumped.jpg The Attempt at a Solution I'm stumped...

Homework Statement Find the area of the parallelogram with vertices: P(0,0,0), Q(-3,0,-1), R(-3,1,0), S(-6,1,-1) Homework Equations A=BH The Attempt at a Solution I think I know why this is incorrect, but i don't know what else to try. I found vector PQ and called it a...

Homework Statement Find the area of the parallelogram with diagonals a = 3i + j − 2k and b = i − 3j + 4k The attempt at a solution I know that |x| X |y| will give the area, but will it hold for diagonals? Or do I have to find x and y vectors?

Homework Statement Find two functions f, g \in C[0,1] (i.e. continuous functions on [0,1]) which do not satisfy 2 ||f||^2_{sup} + 2 ||g||^2_{sup} = ||f+g||^2_{sup} + ||f-g||^2_{sup} (where || \cdot ||_{sup} is the supremum or infinity norm) Homework Equations Parallelogram identity...

Homework Statement Let Ω ⊂ R^2 be the parallelogram with vertices at (1,0), (3,-1), (4,0) and (2,1). Evaluate ∫∫_Ω e^x dxdy. Hint: It may be helpful to transform the integral by a suitable (affine) linear change of variables.Homework Equations The Attempt at a Solution Ok here is what I have...

Homework Statement http://folk.uio.no/robinbj/gg/ggstart.pdf" I am supposed to find the area of the triangle PQD. The numbers given are the areas of the other triangles.Homework Equations A= \frac{1}{2} a b \sin{C} As well as Heron's formula, possibly? A= \sqrt{s(s-a)(s-b)(s-c)} where s =...

Homework Statement ABCD is a paralleelogram.angle DAE=angleEAB and angle CBE=angleEBA .Prove that AB=2BC Homework Equations none The Attempt at a Solution I just got that angle AEB =90 degrees (But it isn't of any help) Please help !

Homework Statement Show that the sum of the squared side lengths of a parallelogram is equal to the sum of its squared diagonals. 2. Somewhat relevant thoughts I've decided to try to show the parallelogram law with vectors, since I already managed to find an Elements-inspired proof of it...

Homework Statement P1(x1,y1), P2(x2,y2), P3(x3,y3), P4(x4,y4) are the vertices of a quadrilateral. Show that the quadrilateral formed by joining the midpoints of adjacent sides is a parallelogram. Homework Equations Midpoint: M = ((x0+x1)/2, (y0+y1)/2) The Attempt at a Solution...

Homework Statement The following theorem in geometry suggests a vector identity involving three vectors A, B, and C. Guess the identity and prove that it holds for vectors in Vn. This provides a proof of the theorem by vector methods. "The sum of the squares of the sides of any...

Let V be a vector space over the complex field. If V has an inner product <\cdot,\cdot>, and ||\cdot|| is the induced norm, then it's easy to show that the norm must satisfy the parallelogram law, to wit: ||x+y||^2 + ||x-y||^2 = 2||x||^2 + 2||y||^2 Much more interestingly, given an arbitrary...

Homework Statement Determine the area of the parallelogram spanned by the vectors < 0, 9, 6 > and < −10, −6, −4 > Homework Equations Area = A X B The cross product of < 0, 9, 6 > and < −10, −6, −4 > = 0i - 60j + 90k The Attempt at a Solution I know the area is the cross...

I am not sure if this question should be in here but it does pertain more to these problems as compared to a general math question. So, could someone explain why when using the parallelogram rule for obtaining the sum of 2 forces by the means of the Law of Cosines that the controller -2bc is...

Homework Statement A parallellogram ABCD has an interior point O sucht that \alpha + \beta = 180^o http://img413.imageshack.us/img413/5636/post102741235319763.png Prove that: \angle{OBC}=\angle{CDO} Homework Equations Definitions of a parallellogram. The Attempt...

Homework Statement let v = (1,0,1) and u = (0,2,1) Find the area of the parallelogram {sv + tu : 0 <= s, t <=1) Homework Equations The Attempt at a Solution I know the area of a parallelogram is the determinant of a 2x2 matrix, but they gave v and u in R^3. Would I just...

Homework Statement This isn't really homework, but a not assigned problem out of my mathbook which is kinda confusing me.. #74. We have two pairs of parallel lines in R^2 defined by the linear equations below: a1x + b1y = r1 a1x + b1y = s1 a2x + b2y = r2 a2x + b2y = s2 We assume...

Use the given transformation to evaluate the given integral, where R is the parallelogram with vertices (-2, 2), (2, -2), (4, 0), and (0, 4). ∫∫(2x+8y)dA; x=1/2(u+v) y=1/2(v-u) I found the bounds of the parallelogram of -4≤u≤4 and 4≤v≤0 so i set the equation to be...

Homework Statement given the vertices: (0,0) (3,1) (2,3) (5,4) Homework Equations solving without cross products and with mathematica if available The Attempt at a Solution Te1=[3] [1] Te2=[2] [3] [det[Ay]] ________ [det[A]] get you the solution...

i'm posting this problem in the calculus forum because i got this question in a calculus class. It seems like a straightforward area problem, but i don't think that's the case and i can't figure out another way to do the problem using vectors. "Find the area of the parallelogram with vertices...

I need to find the area of a parallelogram with two vectors in R^4 my book has nothing on this and I don't know how to do it.

Homework Statement I'm having trouble with a word problem involving the parallelogram law of vector addition. The problem reads as follows: Two forces with magnitudes 8N and 11N act on a large object. The angle between the forces is 30 degrees. a) Draw a diagram to represent the combined...

Homework Statement Given a parallelogram ABCD has vertices A(-1,2,-1), B(2,-1,3) and D(-3,1-3). Find the coordinates of C. Homework Equations The Attempt at a Solution I'm extremely confused here. I do not know how to tell which coordinate is for which vertex on the parallelogram. I...

My girlfriend bought me some sweet astro-binoculars from Orion for Christmas (20x80s) and I would love to use them but they are heavy as hell (and shaky). I was looking around for one of those parallelogram mounts. I found a couple like...

Homework Statement Parallelogram ABCD is given, with A(2,4), B(5,7), C(12,8). Find the coordinates of D(x,y). Homework Equations The Attempt at a Solution Sorry but, I don't have any idea.

Homework Statement Given is a parallelogram which has diagonals of the length 7 (e) and 9 units (f). How big is its circumference? The sides are a,b,c,d; a being the bottom side, rest is anti-clockwise... alpha is the angle of a etc... Homework Equations no are given, i guess...

Homework Statement My professor stated the theorem "If (X,<,>) is an an inner product space and || || is the norm generated by <,>, then we have ||x+y||² + ||x-y||² = 2(||x||² + ||y||²)." But then she also said that the converse was true. I suppose this means that "Given (X, || ||) a normed...

Proof of parallelogram theorem "If 2 pairs of opposite angles congruent, then par..." I was just wondering, why exactly does "If 2 pairs of opposite angles congruent" prove that a quadrilateral is a parallelogram? Does it have something to do with the fact that the sum of the interiors equals...

The vectors 39.0 cm at 15.0° and 23.0 cm at 68.0° both start from the origin. Both angles are measured counterclockwise from the x axis. The vectors form two sides of a parallelogram. a) Find the area of the parallelogram. 716cm^2 b) Find the length of its longer diagonal. For b) is this...

[SOLVED] Help with proving a quadrilateral is a parallelogram. Hi this is my first post here and I'm glad to see that this is a well visited board. I'm having trouble with this one proof though that I have to do for geometry due tomorrow. Only a few other people I know have been assigned this...