2
votes
1answer
26 views

Rotation of conics sections using linear algebra

When given an equation of the form $$Ax^2+Bxy+Cy^2 + Dx + Ey + F$$ where $B \not= 0$ and it is not a degenerate conic, then you can use $\Delta = B^2 -4AC $ to see what type of conic it is, and then ...
0
votes
1answer
49 views

How to find the equation of a line which intersects these lines at 90 degrees?

How to find the equation of a line which intersects these lines at 90 degrees? $p\equiv \dfrac{x}{2}=\dfrac{y+1}{0}=\dfrac{z-2}{1}$ $q\equiv \dfrac{x-1}{1}=\dfrac{y-2}{1}=\dfrac{z+5}{0}$ Since the ...
0
votes
0answers
35 views

Algebra Problem, shortest distance from a point and a line

Find the shortest distance between the point $(-2,1,5)$ and the line $x =(1,2,-5)+ \lambda(6,3,-4)$.
0
votes
1answer
25 views

Find all the intersection points of a vector parabola (in R3) and a sphere

Given that I have a vector in R3 (7t, 10t - 2t^2, 5t) | (These numbers are arbitrary for the sake of the process) A sphere centered at the point ( 15, 25, 10) with a radius of 20 There is a ...
1
vote
1answer
65 views

Find the shaded areas A1, A2, A3

I think i know how to find the angles KAG and KAH that's what i did: (this is the picture from my assignment sheet) then i have to find the shades areas A1,A2 and A3 but i don't know how to ...
1
vote
1answer
69 views

sketch the line segment whose parametric equations

Sketch the line segment whose parametric equations are $x=2+t, v=t^2-1, t∈[0,3]$ That's what i did $t=x-2$ $v=(x-2)^2-1$ $v=x^2-4x+3 $ $v=(x-3)(x-1)$ $x=3,1$ and that's my sketch I am not ...
0
votes
1answer
73 views

Find a vector equation and parametric equations or the line in R^3 that passes through the point (1,2,-3) and is parallel to the vector u=(4,-5,1).

Find a vector equation and parametric equations or the line in $\mathbb{R}^3$ that passes through the point $(1,2,-3)$ and is parallel to the vector $u=(4,-5,1)$. Find two points on the line that are ...
0
votes
1answer
79 views

Find a vector equation and parametric equations of the line in $\mathbb{R}^2$ passing through the origin and is parallel to the vector $\vec{u}=(2,3)$

anyone can help me? :< Are there any equations that I could use in this question? I am so confused. I only know how to do the question if it changes "parallel" to "perpendicular" because I only ...
-1
votes
2answers
121 views

Identifiying the next point on the surface of a cube ( or 3D object )

I have a cube of unit length. Each face of the cube is divided into 10 x 10 equal segments. Consider an object of size equal to that of a segment moving through the surface of the cube ( or any 3D ...
0
votes
1answer
39 views

When can I use a parameter in equation (of the a plane)

In my book there is an example: Find vector and parametric equation of the plane $x-y+2z=5$ Now, the solution is: solving for $x$ in terms of $y$ and $z$ yields $x = 5+y-2z$ and then using parameters ...
0
votes
1answer
345 views

Assignment: Find the number of parameters in the general solution to a system of linear equations

This is a question given in an assignment I'm working on: If the coefficient matrix $A$ in a homogeneous system of 33 equations with 28 unknowns is known to have rank 12, how many parameters are ...
1
vote
3answers
51 views

Is what I'm doing valid?

Find the POI of the following two planes: $$\pi_1: -3x + 3y + z + 6= 0$$ $$\pi_2: 3x - y + 2z - 2 = 0$$ I started by isolating "$z$". $$\pi_1: z = 3x - 3y - 6$$ $$\pi_2: z = \frac ...
0
votes
1answer
108 views

Parametric simultaneous equations

I stumbled on this one a few days ago and I'm probably missing something obvious... I basically need to solve those parametric equations for the other coordinate $(x,y)$ other than the point ...
0
votes
1answer
56 views

Find parametrics equations of a line

Consider the line in $R^2$ that is given by the equation $d_1x_1 + d_2x_2 = c$ for numbers $d_1, d_2$ and $c$ in $R$ where $d_1$ and $d_2$ are not both zero. Find parametric equations of the ...
0
votes
1answer
93 views

parabola in homogeneous coordinates

So if I have the parabola Y = X^2, how do I go about representing this homogeneously? I know I can parameterize it as F(t) = (t, t^2), but then what? The reason I ask is because I have a 3*3 matrix ...
0
votes
1answer
1k views

Converting parametric equation to implicit form

So I have the equation defined in homogeneous coordinates $[w; x, y]$ as $[1+t^2; 1-t^2, 2t]$ $$w = 1+t^2$$ $$x = 1-t^2$$ $$y = 2t$$ If I do $w+x-y$ I get $-2t+2$, so $t = -(w+x-y-2)/2$. I was then ...
1
vote
1answer
305 views

converting a parametric R5 vector into a Cartesian form

How do you solve a problem like this. I'm completely stumped. it seems like there should be an easy solution but I'm obviously over looking it. any help would be greatly appreciated.
1
vote
0answers
54 views

Maximum value for parameter

I am facing the following problem: A number of a adults, b children older than 12, and c children younger than twelve attend an event. The sum of all people a+b+c=100. The prices are \$6 per adult, ...
1
vote
1answer
541 views

Parametric Equation

Let $P_1$ be the plane through the origin containing the vectors $[1,2,-1]$ and $[0,1,1]$. Let $P_2$ be the plane through the point $(1,1,1)$ parallel to the vectors $[-1,2,2]$ and $[3,4,-2]$ I know ...
1
vote
2answers
1k views

Give the parametric eqns of the line intersecting the planes

Give the parametric equations of the line of intersection of the planes $$4x + 2y + 2z = -1$$ and $$3x + 6y + 3z = 7$$ Also, give the equation of the plane that passes through the point $(2,-1,4)$ ...
1
vote
1answer
271 views

Doubt with parametric and symmetric equations

In the line through $P(0, 0, 0)$ and is perpendicular to $x=y-5$, $z=2y-3$, when we solve the equations and get the symmetric equations in order to find the vectors $V_1$ and $V_2$, why the normal ...
2
votes
3answers
15k views

Find the equation of the plane passing through a point and a vector orthogonal

I have come across this question that I need a tip for. Find the equation (general form) of the plane passing through the point $P(3,1,6)$ that is orthogonal to the vector $v=(1,7,-2)$. I would ...
3
votes
3answers
3k views

How to convert a plane (e.g. $4x - 3y + 6z = 12$) into parametric vector form?

I can convert something in the 2nd dimension fine, but I'm having difficulty with something like $4x - 3y + 6z = 12$. Any help? EDIT: Solve using only algebra, no matrices yet.