Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t) = (3 sin(t), 4 cos(t)) y 2 1- 1 0000 1 2 3 4 5 -4 -2 -1 -1- -2 0 - 4 -3 -2 -1 3 2 1 -1- -2 -3 1 2 4 -5-4-3-2-1 2 -1 -2 3 -3 1 2 4 -5-4-3 -2 -1 2 1 -1 -2 1 2 3 5 X

Let r(t)=(10 cos(t), 1, 10 sin(t)). Find the unit tangent vector u drawn to point P-(6,1,8). Sketch curve and tangent.

4) For the following vector functions, identify the shape of graph they would represent: a. r(t) = (2+ 3t, 5, -2-t) b. r(t) = (2, cos(3t), sin(3t)) c. r(t) = (t,5, t²)

At time t = 0, a particle is located at the point (5,9,4). It travels in a straight line to the point (2,1,3), has speed 5 at (5,9,4) and constant acceleration - 3i-8j - k. Find an equation for the position vector r(t) of the particle at time t. The equation for the position vector r(t) of the particle at time t is r(t) = (Type exact answers, using radicals as needed.) i+ j+ k.