



Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
A midterm exam for math 251 at simon fraser university, held on 7 february 2006. The exam contains 5 questions on vector calculations, angular momentum, helical paths, and parametric equations. Students are required to solve problems related to finding vector products, areas, angles, equations of planes, distances, derivatives, and curvature.
Typology: Exams
1 / 6
This page cannot be seen from the preview
Don't miss anything!




Midterm 1 7 February 2006, 5:30–6:20pm
Instructor: Ralf Wittenberg
Instructions
A(1, 2 , 1), B(2, 0 , 1), C(− 1 , 2 , 0), and D(3, 3 , −1) :
(a) [2 points] Compute
−→ AB ×
−→ AC.
(b) [2 points] Find the area of the triangle ABC.
(c) [4 points] Find the angle θ between the vectors
−→ AB and
−→ AC.
(d) [6 points] Find an equation of the plane that passes through A and B and is parallel to the line through C and D.
v(t) = 3 i + 4 sin t j + 4 cos t k , t ≥ 0.
(a) [3 points] At time t = 0, the particle passes through the point P (1, 0 , 0). Find the position vector r(t) for the particle.
(b) [3 points] Find the distance travelled (arc length) along the helical curve from t = 0 to t = 2π.
(c) [4 points] Find the tangent vector T and principal normal vector N to the helical curve.
x = t, y = t^2 , z = 43 t^3 /^2 , t > 0.
(a) [4 points] Find the velocity and acceleration vectors, and the speed of the particle as a function of t.
(b) [6 points] Determine the curvature κ and radius of curvature of the curve traced out by the particle at time t = 1.