There are an infinite number of vector and parametric equations for a given plane. Why is...

There are an infinite number of vector and parametric equations for a given plane. Why is the scalar equation of a given plane unique?

Expert Solution

milcah answered 2 years ago

Find the vector and parametric equations for the plane. The plane that contains the lines r1(t)...

Find the vector and parametric equations for the plane. The plane that contains the lines r1(t) = <6, 8, 8,> + t<-2, 9, 6> and r2 = <6, 8, 8> + t<5, 1, 7>.

Find parametric equations for the tangent line to the curve with the given parametric equations at...

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector $\mathbf{T}$, the principal unit normal $\mathbf{N}$, and the curvature $\kappa$ for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$

Find the equation of the tangent plane and the parametric equations for the normal line to...

Find the equation of the tangent plane and the parametric equations for the normal line to the surface x2 + y2 - z = 0 at the point P(4,-1, 6). Show all steps

1. a.) determine vector and parametric equations for the line through the point A(2, 5) with...

1. a.) determine vector and parametric equations for the line through the point A(2, 5) with direction vector = (1, −3). b.)Determine a vector equation for the line through the points (-1, 4) and (2, -1). c.) Determine parametric equations for the line through (-2, 3) and parallel to the line with vector equation = (−2, 1) + t(6, 4). d .) A line passes through the point (-4, 1) and is perpendicular to the line with parametric equations...

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line...

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (2, 2.9, 3.6) and parallel to the vector 3i + 4j − k r(t) = (x(t), y(t), z(t)) =

1. Given parametric equations below, find the values of t where the the parametric curve has...

1. Given parametric equations below, find the values of t where the the parametric curve has a horizontal and vertical tangents. a) x=t^2 - t, y= t^2 + t b) x= e^(t/10)cos(t), y= e^(t/10)sin(t) 2. Find the arc length of the graph of the parametric equations on the given intervals. a) x= 4t+2, y = 1-3t , −1 ≤ t ≤ 1 b) x= e^(t/10)cos(t), y= e^(t/10)sin(t), 0 ≤ t ≤ 2π

1. Given parametric equations below, find dy/dx , equations of the tangent and normal line at...

1. Given parametric equations below, find dy/dx , equations of the tangent and normal line at the given point. (a) x = t^2 , y = t^3−3t at t = 1 (b) x = cos(t), y = sin(2t) at t = π/4 2. ) Given parametric equations below, find d^2y/dx^2 and determine the intervals on which the graph of the curve is concave up or concave down. (a) x = t^2 , y = t^3−3t (b) x = cos(t), y...

Question: (a) Find parametric equations for the line of intersection of the planes given by 3x...

Question: (a) Find parametric equations for the line of intersection of the planes given by 3x − 2y + z = 1 and 2x + y − 3z = 3. (b) Find the equation of the plane orthogonal to both of these planes and passing through the point (−2, 1, 1).

Given an infinite sheet of charge occupying the x-y plane such that the charge density is...

Given an infinite sheet of charge occupying the x-y plane such that the charge density is constant and uniform, find the electric field at any point on the z-axis by: A) Using the point charge formula for the electric field directly in cartesian coordinates. B) Using the point charge formula for the electric field directly in cylindrical coordinates. C) Using the point charge formula for potential in cylindrical coordinates and taking the gradient. DO NOT USE GAUSS'S LAW

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