four points Definition and 11 Threads

Hi, i'm trying to solve this problem. It's exercise 3 on page 5 from this book: Challenging mathematical problem with elementary solutions The solution is on page 41: I'm OK with the 4 circles in case 1: i can pick (inside/outside): ABC + D, ABD + C, ADC + B, BCD + A. What i cannot...

How do you find the equation of a plane in determined by say three or four points in $\mathbb{R}^4$? In $\mathbb{R}^{3}$ we would use the cross product to find normal vector, but that doesn't apply in $\mathbb{R}^4$.

Homework Statement (2; 0; 1); (-1; 2; 3); (3; 2; 2) and (3;-6;-3) Homework Equations PS→⋅(PR→×PQ→)=0 The Attempt at a Solution Hi all, I am just wondering if my calculations are correct, and in fact these points do not lie on a plane. My answer is = 50 and i am not confident. Can...

I am working on finding the area of a solid object. I have 4 points that I need to calculate a cubic equation from. I have tried relentlessly but to no avail I always get the wrong answer. The four points are;(0,2.7) (0.5, 2.9) (1,3.2) (1.9, 3.4) Using excel, the formula should be...

Hi all, If a,b,c,d are position vectors of four points A,B,C,D.The points will be coplanar if xa+yb+zc+td=0,x+y+z+t=0,provided x,y,z,t are not all 0,and they are scalars.Is this test needed to show 4 points are coplanar? If we consider two lines joining A,B and C,D then this will give us two...

Hello, I am no mechanical engineer and my knowledge in bending is limited to Euler-Bernouilli beam theory. I wish to analytically calculate the normal stress of a plate bent by four points bending. I have already calculated this stress for a beam. However I cannot apply the beam theory...

The problem is: A, B, C, D are any four points in space. If M and N are the mid-points of AC and BD, show that AB + CB + CD = 4MN. I'm not quite sure where to start. Could someone please help me?

Homework Statement Draw a diagram to show that there are two lines tangent to both of the parabolas y = - x^{2} (1) and y = 4 + x^{2} (2) Find the coordinates of the four points at which these tangents touch the parabolas. Homework Equations y - y_{o} = m(x - x_{o}) The Attempt at a...

How do you determine Coplanarity of four points? I am given A(3,1,0), B(2,-3,1), C(-1,0,4), D(5,-6,-2). Do i make vectors for each point from the origin? (But that wouldn't work would it? :() Can anybody point me in the right direction? Thanks!

Homework Statement Find the radius and center for the sphere determined by the four points (3,2,-1), (5,-2,1), (-3,1,2), (0,2,4). Give the exact location of the center but approximate the radius to the nearest 0.1.Homework Equations Equation of a sphere: x2 + y2 + z2 + Gx +Hy +Iz +J = 0 or...

Homework Statement Find the ratio EH:HG. Please, see the full question with a picture here: https://dl.getdropbox.com/u/175588/problem.JPG Homework Equations "In triangle ABC, let D and E be the trisection points of BC with D between B and E." Please, see the full question with a picture...