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Material Science

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FDM 1033 VECTOR CALCULUS (September 2014 Semester)
Assignment 1 (5%)- 21st October 2014
Submission date: 3rd November, 2014
(a) Let L1 be the line through (1, -6, 2) with direction vector
<1, 2, 1> and L2 be the line through (0, 4, 1) with direction vector <2, 1, 2>. Determine if the lines are parallel, if they are intersect or if they are skew. If they intersect, find the point at which they intersect.
(b) Find the angle between the line L1 and L2.
(c) Find the points at which L1 intersects with the coordinate planes. [15 marks]

Given r ( t ) 

 cos t ,

sin t ,

ln cos t  .

Find the vectors T, N and B at the

point (1, 0, 0).
[10 marks]

The height of a tree increases at a rate of 2ft per year and the radius increases at 0.1 ft per year. What rate is the volume of timber increasing at when the height is 20 ft and the radius is
1.5 ft. (Assume the tree is a circular cylinder).
[10 marks]
A Cobb-Douglas production function for new company is given by


f ( x , y )  50 x 5 y 5










represents the units of capital. Suppose units of Labor and capital cost $100 and $200 each respectively. If the budget constraint is
$30,000, find the maximum production level for this manufacture.

[15 marks]

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