A particle is traveling on a path that is defined by the vector function given b

Question

A particle is traveling on a path that is defined by the vector function given below. r(f) = (sin (t), cos (t), sin (t) cos (2t), -pi t pi 5) Find at least two points where r(f) intersects the xy-plane. 6) Click the Blackboard RESOURCES button (under Section 13.1 - Graphing Space Curves) to go to http://www.flashandmath.com/mathlets/multicalc/paramrec/index.html. Graph r(f) and find its projections onto the xy-, xz-, and yz- planes. Attach screen prints of the graph of r(t) and its three projections; showing any fields where you typed in parametric functions, ranges, etc.

Explanation / Answer

5)r(t)=<sin(t),cos(t),sin(t)cos(2t)>

-pi<=x<=pi

=>-2pi<=2x<=2pi

when r(t) intersects xy plane, z coordinate is 0

sin(t)cos(2t)=0

sint =0

=>t =-pi,0,pi

cos(2t)=0

=>2t=-3pi/2,-pi/2,pi/2,3pi/2

=>t=-3pi/4,-pi/4,pi/4,3pi/4

at t =-pi,0,pi ,-3pi/4,-pi/4,pi/4,3pi/4

for 2 points , letus take t =0 , t=pi

t =0

=>point of intersection =(sin(0),cos(0),sin(0)cos(0))

=>point of intersection =(0,1,0)

t =pi

=>point of intersection =(sin(pi),cos(pi),sin(pi)cos(2pi))

=>point of intersection =(0,-1,0)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.