Math53, Spring 2008 Wednesday, February 13, 2008
Section 108/109 Matthias Goerner
Problems from previous midterms
1. The plane curve Chas parametric representation
x= cos t, y = sin 2t, 0≤t≤2π.
Compute the equation of the tangent line at the point (x, y) = (√3
2,√3
2).
Sketch the curve Cand the tangent line.
2. A line has the vector equation
r(t) = i+j+k+ (j+k)t.
Find the point pin this line so that the displacement vector from the
origin to pis perpendicular to the line.
3. Compute the equation of the plane which passes through the point
(1,1,1) and contains the line whose parametric equations are
x=t, y = 2t, z = 3t.
4. The space curve Chas the vector equation
r(t) = (i+j) cos t+ (j+k) sin t, 0≤t≤2π.
What points on Care furthest from the origin?
1
