# Vector calculus problem

• Apr 21st 2010, 01:39 PM
bobmarley909
Vector calculus problem
1. Let the trajectory be defined by parameter t, as follows: x(t)=2Cost, y(t)=2Sint, z(t)=3t.
a) Sketch the trajectory in 3d space.
b) Calculate the unit tangent vector at t=\$\displaystyle pi\$
c) Find the equation of the plane perpendicular to the trajectory at t=\$\displaystyle pi\$
d) Calculate the length of the curve defined by 0<(or equal to)t<(or equal to)5

Any help would be appreciated.
I do not know how to begin.
• Apr 22nd 2010, 09:24 AM
HallsofIvy
It's hard to know what help you need if you don't show what you have done or what you do know about this. Do you know how to find the tangent vector? Do you know how to find the equation of a plane perpendicular to a line? Do you know a formula for arclength?

As for the graph note that \$\displaystyle x^2+ y^2= 4cos^2t+ 4 sin^2t= 4\$ is a circle in the xy- plane. That means the curve is directly above that circle while z increases. What figure is that?