Math 4C -- Lab 2: Vector Calculations NAME ______________
1. Use Maple to
a. Define the vectors u:=[1,-3,5] and v:=[-1,4,6];
b. Find the norms of u and v. Example: norm(u,2); Note: the 2 is needed in Maple (to find the second root of the sum of the second powers).
c. Write a vector in the direction of v with the length of u.
d. Calculate the angle between u and v. (Give its cosine, and then a decimal approximation of its radian measure.)
e. Find the area of the triangle determined by u and v.
f. Find an equation of the plane containing u, v, and the point (1,-2,6).
2. Use Maple to
a. Define the vector r:=[4t, 3cos(t),3sin(t)].
b. Sketch the space curve defined by r from t=0 to t=4π. Use the tubeplot instruction.
c. Calculate the following:
(1). r¢(t) Tangent vector or velocity vector (call it v)
(2). r¢¢(t) Acceleration vector (call it a)
(3). Unit tangent vector
(4). Arc length from t=0 to t=2p
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Updated 06/13/06 by Don Power