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MATH 2D (200)

WILKINSON, J (10)

Lecture 10

Department

MathematicsCourse Code

MATH 2DProfessor

WILKINSON, JLecture

10This

**preview**shows pages 1-2. to view the full**8 pages of the document.**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 ≤t≤2π

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2. For the vectors ~a = [3,2,4],~

b= [−1,2,1],~c = [3,1,−3] calculate:

~a + 2~

b−4~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 4x−y+z= 2 and 4x−y+z= 14

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