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
Suppose u=(-2,-10) and v=(-2,-2) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are...
Homework Equations
The Attempt at a Solution
I tried using pythagrean theorem and some trig to find the...
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...
Hi guys,
I want to check that I am going about this problem in the right way:
The attached image shows a parallelogram type frame with a hydraulic ram located from corner to corner as shown (E to C). There is a load applied to a platform in the far bottom right hand side of the drawing...
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...
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...