The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find the speed of the particle at time to = 4. (b) Is c'(t) ever orthogonal to c(t)? O Yes, when t is a multiple of T. O Yes, when t = 0. O No (c) Find a parametrization for the tangent line to c(t) at to = 47. (Enter your answer as a comma-separated list of equations in (x, y, z) coordinates.) (d) Where will this line intersect the xy-plane? =([ (x, y, z) =

Q: The parametric equations of a curve is * = cos(t), y = sin(t – t) (a) find the equation of the…

A:

Q: The parametric equations of a curve is x = = 3 sint, y = 3 cost and z = 4. (a) Sketch the curve r(t)…

A: The given parametric curve is x=3sint, y=3cost, z=4. (a).  To draw the given curve rt=3sint, 3cost,…

Q: x(t) = 3 cos t y(t) = 8 sin t 0<t< 2n a) What does the curve described by these parametric equations…

A:

Q: The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find…

A: The position vector for particle moving on helix is ct=3cost, 2sint, t2. To find the speed of the…

Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

A:

Q: Find torsion of the motion r(t) = . Leave your answer correct to two decimal places.

A:

Q: Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a…

A: To find The parametric equations for the line that is tangent to the given curve

Q: x(t) y(t) = 3 sin t 8 cos t 0<t< 2n a) What does the curve described by these parametric equations…

A: Recall: Equation of line: y-y1=mx-x1 ; where m=dydx or  y2-y1x2-x1 Length of the curve…

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: The position vector of a particle moving along a helix is = = 4TT. c(t) = (cos(t), sin(t), t²). (a)…

A:

Q: Q4. A point is moving along a curve that is given as: R(1) = {cos 31 )i + (sin 31) j + (31)k. Find:…

A: Given position vector is R→t = cos3t i +sin3t j +3t k Function fx, y, z =x y z

Q: Sa(t) = t2 – 3 lu(t) = 2t +1' Consider the parametric curve -2 <t< 3. At which time(s) does the…

A:

Q: Which is a parametric equation for the curve 25 = (x +7) + (y+ A. c(t) = (5 cos(t) – 5, 5 sin(t) –…

A:

Q: [x(t) = 3t² – 3 v(t) = 2t +1 Find the slope of the tangent to the parametric equations at t=1.

A:

Q: The parametric equations of a curve is x = 3 sin t, y=3 cos t and z = 4. (a) Sketch the curve r(t)…

A:

Q: 1. The parametric equations for the astroid below are x = sin' (t), y =- cos (1) on 0<t < 2a. a)…

A: Given, the parametric equation for the astroid below are  First need to find the stating point on…

Q: Find the unit tangent vector to the curve defined by F(t) = (5 cos(t), 5 sin(t), 2 sin²(t)) at t = 5…

A:

Q: Draw the projection of the vector-valued curve r(t) = (1, 4 cos (21), -7 sin (61)) on the xy- plane.…

A: