l. 2. 3. 4. 5. 6. 7. 8. HW4.l Vector Functions - cuwes & derivatives & integrals sint For cost (a) what graph is seen in the xy-plane perspective? (b) what graph is seen in the xz-plane perspective? (c) what graph is seen in the yz-plane perspective? (t+3+3t4, arctan(t)+2, -2+tet), (a) find n ' (b) find the equation of the For the vector tangent line at t=0 (2e3t t2-4t, In(t+l)) find (a) the velocity and its magnitude (b) For the position vector the acceleration and its magnitude 2 t For the velocity vector fimction 5 5t find the position vector function if the e position is the origin at t=0. = (e3t, I-t2, 3t-4t4)find F (t) if for i ' 2 t3 ) for = (t, 0.2t5, find the arc length of 3 [**] A projectile is launched from flat ground with initial velocity vector which makes an angle a with the ground. The only acceleration is due to gravity, g. Show that, when it lands, it has traveled a horizontal distance of sin 2 a [you can prove it using only calculations with the given and no fonnulas from physics] [*] for position vector = (t2-l, 3-2t, 4t-t3) find [*] the unit tangent [ ** ] the unit nonnal, the binormal, and the curvature