Math 1220
Instructor: Mike Shrieve
Practice Midterm #1
Name:
The midterm is 50 minutes. No calculators or equation sheets are allowed. Answer all
questions.
(1) Let ~u = h4, 2, −7i and ~v = h−1, 3, 6i. Calculate the following:
(a) ~u + ~v
(b) ~u · ~v
(c) ~u × ~v
(d) Proj~v ~u
(2) Write an equation for the plane passing through the points (1, 4, 5), (−2, 6, −1), and
(0, 0, 0).
(3) Write an equation for the plane passing through the origin which is orthogonal to
both the plane x + y + z = 7 and the plane 4x − 2y = 1.
(4) Write a parametric equation for the tangent line to the curve given by the vector
function ~r(t) = ht2 , 7t, 4t − 1i at t = 4.