Math 271
Final (Version 1)
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(1) Find an equation of the line through (1, 1, 2) and intersects the line
x = t 3
at a right angle. (10)
y =t6
z = t + 8
(2) Find the unit tangent vector T and the unit normal vector N for
(t)
Math 271
Final (Version 2)
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(1) Find parametric equation of the line through (1, 0, 2) and parallel to the
2x y = 3
line
(10)
x + 2y 2z = 8.
(2) Find the unit tangent vector T and the unit normal vector N for
(t) = (2 sin
Math 271
Final (Version 3)
Name.J Number.Score.
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(1) Find an equation of the line through (1, 1, 2) and intersects the line
x = t 3
at a right angle. (10)
y =t6
z = t + 8
(2) Find the limits. (10)
(a). lim(x,y)(0,0) 3xy 2 ;
2
x +4y
2
(3)
(4)
Math 271
Final (Version 4)
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x = t
(1) Find an equation of the plane that contains the line y = 2t + 3
z = t + 8
x1
parallel to the line 2 = y = z . (10)
(2) Find the limits. (10)
, and
x2 +4y 2 +42
(a). lim(x,y)(0,0)
;