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MATH 2D (200)
Lecture 10

# MATH 2D Lecture Notes - Lecture 10: Parametric Equation, Unit VectorExamPremium

Department
Mathematics
Course Code
MATH 2D
Professor
WILKINSON, J
Lecture
10

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Math 2D Practice Midterm 1
1. Consider the parametric curve x(t) = 1 + 2 sin(t) and y(t) = 3 4 cos(t)
(a) Find the rectangular form of this curve by eliminating the parameter.
(b) Sketch the graph of the curve on the axes below.
(c) Set up the integral representing the arc length of the curve for 0 t2π

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2. For the vectors ~a = [3,2,4],~
b= [1,2,1],~c = [3,1,3] calculate:
~a + 2~
b4~c ~a ·~
b+~c~c ×~
k
Find a unit vector in the direction of ~a
What is the angle between ~
band ~c?

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3. (a) Find the equation plane containing the point (1,0,5) and the line L(t) = [1, t 1, t + 2]
(b) Find the distance between the planes 4xy+z= 2 and 4xy+z= 14