0
votes
0answers
14 views

Find the intersection of three bisection lines

Let $p_1 = (a_1, b_1), p_2 = (a_2, b_2), p_3 = (a_3, b_3)$ be three, non-colinear points in the plane. For each pair of these points, let $L_{ij}$ denote the line segment from $p_i$ to $p_j$. (a) For ...
1
vote
1answer
29 views

Convex Sets and extreme supports

Let the set $S$ in $R^n$ consists of the origin $0$ and $n$ lineary independent vectors $T_1, \ldots, T_n$. Show that $C(S)$, the convex hull of of $S$, is the intersection of its extreme supports, ...
3
votes
3answers
216 views

What is wrong with this method for a rotated and shifted parabola?

$(x+2y)^2=4(x-y)$ Disecting the above parabola is the question. (vertex, axis,tangent at vertex,etc). So at first what I thought of was making its equations at LHS and RHS perpendicular. I thought ...
1
vote
1answer
30 views

How to get coordinates of some area

I have a rectangle and I divide it into 8 triangle with same size. Top left corner is origin. I want to check that if a point is inside the black area or not. Lets say point's x coordinate is pointX ...
1
vote
1answer
31 views

Locus of center of circle.

Consider two circles with radii $a$ and $b$ and centers $(a, 0)$ and $(b, 0)$ respectively with $0 < a < b$. Let $c$ be the center of any circle in the crescent shaped region M between the two ...
0
votes
1answer
32 views

What are the coordinates of the ends of the latus rectum of the parabola $x^2 - 2y + 2 = 0$? [duplicate]

I've already graphed the parabola . i just don't know how to locate it's focus and the ends of it's latus rectum. On my graph, the vertex is on (0,1). Please help me with this. ASAP.
0
votes
2answers
51 views

How to find the x-component of a spherical vector?

I am given the point $P(r=0.89, \theta=30^\omicron, \phi=45^\omicron)$ and $\vec E=1/r^2(cos(\phi)\hat a_r +sin(\theta)\hat a_\phi)$. Find the x-component of $\vec E$ at $P$. I found the vector in ...
0
votes
0answers
14 views

Z Spec - How to constrain X Y Coordinates

I'm trying to build a system state schema in Z spec that specifies the following: Points of interest use (X,Y) coordinates to specify their location. a small point of interest exists that only has 1 ...
0
votes
2answers
33 views

How to work out the unknown vertex of a parallelogram given the other three

I have changed the numbers so you're not giving me the answers. Let A (1, 1), B (5,2), C (2, 4) and D (x, y) be the vertices of a parallelogram ABCD. What are the coordinates of vertex D? -As I am ...
1
vote
0answers
27 views

equation of a refracted straight line

we have got a line $$x-y=1$$ which after refracting from $x$-axis bends at angle $\pi/6$ from normal what's eqation of that line? what i did was that putting $y=0$ to get points on $x$-axis which ...
0
votes
0answers
36 views

Changing cylindrical coordinates to cartesians's

I was wondering how to find $e_r$ using $e_x$ and $e_y$ as you can see in the scheme: So what I really want is to prove that: $$\vec{e_r}=\cos\theta\vec{e_x}+\sin\theta\vec{e_y}$$ with a deep ...
1
vote
1answer
71 views

Integral coordinates Proof

Nine distinct points with all coordinates integral are selected in the space. Prove that the line segment with ends at certain two of these points contains in its interior a point with all coordinates ...
0
votes
5answers
175 views

Help in question related to locus of pair of tangent to a circle?

This the question in my text-book The tangent to $x^2 + y^2 = a^2$ having inclination $\alpha$ and $\beta$ intersect at $P$. If $cot\alpha$ + $cot\beta = 0$, then the locus of $P$ is : i really ...
0
votes
2answers
162 views

Converting $(4,-4{\sqrt3}, 6)$ from rectangular to cylindrical coordinates

I'm getting the wrong answer for $\theta$. What am I doing wrong? $$(4,-4{\sqrt3}, 6)$$ $$r =\sqrt{4^4 + (-4\sqrt{3})^2} = 8$$ $$z = 6$$ $$\tan\theta=\frac{-4\sqrt{3}}{4}$$ $$\tan\theta=-\sqrt{3}$$ ...
1
vote
1answer
471 views

How to determine gradient of vector in cylindrical coordinates?

I am wondering how to actually determine the gradient of a vector in cylindrical coordinates. I have seen a lot of websites that just say what the general form is but I cannot seem to understand how ...
0
votes
0answers
27 views

Natural dihedral

Can you help me with this: A body of mass $m$ is moving under gravitational force and resistance force proportional to the square of its speed. Write differential equations of motion of a body in ...
1
vote
2answers
2k views

Finding a line perpendicular to a line and passing through the intersection of other two lines

So here is the question as in my text book Find the equation of the line through the intersection of $2x - 3y + 4 = 0 $ and $3x + 4y - 5 = 0$ and perpendicular to $6x - 7y + c = 0$ so I ...
-1
votes
1answer
49 views

Confusion on the given solution to a homework question.

Question: If the line $ x = a+m $, $y = -2 $ and $y = mx$ are concurrent, the least value of $|a|$ is (A) $\sqrt{2}$ (B) $2\sqrt{2}$ (C) $2\sqrt{3}$ (D) ...
2
votes
1answer
81 views

Need a hint on what's wrong - polar coordinates

I'm asked to solve the following $$ \int^2_0 \int^\sqrt{4-y²}_0 \sqrt{4-x^2-y^2} dxdy $$ I thought about using polar coordinates: (1) $0 \le x \le \sqrt{4-y^2}$ is the upper half of a circumference ...
0
votes
2answers
188 views

Expansion of velocity in polar coordinates using kinetic equations

Why does total energy $$E=\dfrac{1}{2}\mu\mathbf{v}^2+U(r)$$ expand to $$E=\dfrac{1}{2}\mu(\dot{r}^{2}+r^2\dot{\phi}^2)+U(r)?$$ It's some form of the kinetic equations in polar coordinates. I know ...
0
votes
2answers
96 views

How many coordinates are unreachable?

I wanted to know, if a man was to go from $(0,0)$ to $(46,46)$ moving only straight and up with the following constraints:- If he walks right, he will walk atleast $4$ consecutive coordinates. If ...
0
votes
1answer
43 views

Euclidean space problem

In three-dimensional space, is it true that if you take line $a$ of a plane and line $b$ of the plane perpendicular to the first one, then the angle between line $a$ and $b$ (at which they intersect) ...
0
votes
2answers
36 views

computing the $y_{cm}$

Suppose I have a half disc and the coordinates axes at the centre of base of the disc. For the given system, I have surface mass density $S$ as $$S=S_0 sin\theta$$($S_0$ being positive constant). I ...
0
votes
2answers
50 views

Find the tangent to a function

Find the tangent to this $\displaystyle y={1 \over x+3}$ it's crossing the point $(-2,1)$ I have drawn the lines but I can't calculate it
3
votes
3answers
436 views

Tetrahedron problem (proving)

Prove that if $P$ is the intersection of the altitudes of a tetrahedron $ABCD$ and $r$ is the circumradius then $PA^2+PB^2+PC^2+PD^2=4\cdot r^2$.
0
votes
1answer
214 views

How to determine a Triangle vertices by its coordinates?

I have to solve this problem, yet I'm not sure what is asked. Given a triangle whose vertices are defined by its coordinates. Determine where is the point O with the given coordinates - inside or ...
3
votes
1answer
94 views

Unusual function format and its partial derivatives.

I came across a function of this format: $z = f(u,v)$ where $u = x^2y^2$ and $v = 5x + 1$ Because this function is not in the same format of the ones I've seen before (explicit or implicit), I don't ...
-1
votes
1answer
169 views

Finding Angle Between Lines represented by Homogenous Equations

I am trying to find angle between two lines represented by a homogeneous equation The equation is : $ 7x^2 + 4xy + 4y^2 = 0 $ When i use the standard formula $ \theta = \arctan \frac {2 \sqrt {h^2 ...
1
vote
1answer
296 views

Converting a triangle to Barycentric Coordinates

Given the triangle T = (P1, P2, P3) with P1 = (-2, -1, 1), P2 = (2, 1,-1), and P3 = (3, 0, -4) and with texture (s, t) coordinates at the vertices defined as (0.25, 1.0), (0.8, 0.8), and (0.6, 1.0) ...
1
vote
2answers
65 views

What are $a$ and $b$?

The growth rate of the function $$f(x) = b a ^ x$$ is $17\%$, and $f(0) = 24$ What I am trying to figure out is how to find out what $a$ and $b$ in this equation are?
0
votes
1answer
53 views

Prove that $QM = PN$ [Coordinate Geometry]

If the points $(P,Q)$, $(M,N)$ and $(P-M,Q-N)$ are collinear. Then show that $QM=PN$.   Basic Points and formulae: Distance between two points = $\sqrt{(x_2-x_1)^2+(y_2-y_2)^2} $ Where, ...
2
votes
1answer
717 views

invariance of cross product under coordinates rotation

Question goes as If $\vec A$ and $\vec B$ are invariant under rotation, the prove that $ \vec A \times \vec B $ is also invariant. However solution of on the other page is not given. Says ...
0
votes
1answer
105 views

Find the number of common normals to both these curves.

Find the number of common normals to the curves $ x^2 + (y-1)^2 =1 $ and $y^2=4x$. My take : I formed a cubic in $m$ i.e. slope, so there'll be 3 normals. Please help.
1
vote
5answers
4k views

Find out the differential equation of the following families of curves.

Find out the differential equation of the following two families of curves : Straight lines having slope and $x$-intercept equal in magnitude. Straight lines at a fixed distance $p$ from the origin. ...
2
votes
1answer
2k views

building transformation matrix from spherical to cartesian coordinate system

How to arrive at the following from given $ x = r\sin \theta \cos \phi, y = r\sin \theta \sin \phi, z=r\cos\theta $ $$ \begin{bmatrix} A_x\\ A_y\\ A_z \end{bmatrix} = \begin{bmatrix} \sin ...
2
votes
2answers
237 views

Triangle related coordinate geometry question

Given triangle $\triangle ABC$ , with $AB=AC$ and 2 times(length of inradius) which is equal to the length of exradius of excirle opposite vertex $A$. Setup the coordinate system in the plane ...
0
votes
1answer
2k views

Finding an equation of a sphere for a specific plane

I am not sure how to proceed with this question from Stewart's SV Calculus text: Find equations of the sphere's with center $(2, -3, 6)$ that touch (a) the $xy$-plane, (b) the $yz$-plane, (c) ...
1
vote
1answer
114 views

Movement in a grid

I am in a middle of a grid of 8X8 . Each box of grid is a square with side of 80 units. Suppose my current coordinates are 594,422 . How many boxes will i have to move to enter the square that ...