Find the distance between the skew lines with parametric equations x = 1 + t, y...

Find the distance between the skew lines with parametric equations x = 1 + t, y = 3 + 6t, z = 2t, and

x = 1 + 2s, y = 6 + 15s, z = −2 + 6s.

Find the equation of the line that passes through the points on the two lines where the shortest distance is measured.

Expert Solution

Colby Messinger answered 2 years ago

Find the distance between the skew lines with the given parametric equations. x = 2 +...

Find the distance between the skew lines with the given parametric equations. x = 2 + t, y = 3 + 6t, z = 2t x = 1 + 4s, y = 5 + 15s, z = -2 + 6s.

Find the distance between the skew lines given by the following parametric equations: L1: x=2t y=4t...

Find the distance between the skew lines given by the following parametric equations: L1: x=2t y=4t z=6t L2: x=1-s y=4+s z=-1+s

The cycloid has parametric equations x = a(t + sin t), y = a(1 - cos...

The cycloid has parametric equations x = a(t + sin t), y = a(1 - cos t). Find the length of the arc from t = 0 to t = pi. [ Hint: 1 + cosA = 2 cos2 A/2 ]. and the arc length of a parametric

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>.

Consider the curve traced out by the parametric equations: { x = 1 + cos(t) y...

Consider the curve traced out by the parametric equations: { x = 1 + cos(t) y = t + sin(t) for 0 ≤ t ≤ 4π. 1. Show that that dy dx = − 1 + cos(t)/sin(t) = − csc(t) − cot(t). 2. Make a Sign Diagram for dy dx to find the intervals of t over which C is increasing or decreasing. • C is increasing on: • C is decreasing on: 3. Show that d2y/dx2 = − csc2...

Consider the parametric curve given by the equations x = tsin(t) and y = tcos(t) for...

Consider the parametric curve given by the equations x = tsin(t) and y = tcos(t) for 0 ≤ t ≤ 1 Find the slope of a tangent line to this curve when t = 1. Find the arclength of this curve (make sure to do it by integration by parts if you ﬁnd yourself integrating powers of sec(θ))

Consider the line L with parametric equations x = 5t − 2, y = −t +...

Consider the line L with parametric equations x = 5t − 2, y = −t + 4, z= 2t + 5. Consider the plane P given by the equation x+3y−z=6. Find the distance from L to P .

3. Given the parametric equations x = 3t /1 + t^3 and y = 3t^2 /1...

3. Given the parametric equations x = 3t /1 + t^3 and y = 3t^2 /1 + t^3 . a) Show that the curve produced also satisfies the equation x^3 + y^3 = 3xy. b) Compute the limits of x and y as t approaches −1: i. from the left ii. from the right c) To avoid the issue in part b), graph the curve twice in the same command, once for −5 < t < −1.5 and once for...

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t...

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Use a graphing device to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.)

A curve c is defined by the parametric equations x= t^2 y= t^3-4t a) The curve...

A curve c is defined by the parametric equations x= t^2 y= t^3-4t a) The curve C has 2 tangent lines at the point (6,0). Find their equations. b) Find the points on C where the tangent line is vertical and where it is horizontal.

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