I have this multiple choice question and I was wondering if I'm getting the answer right.
"If r(t) = <t^3, t>, you should know enough about the concavity to determine N(1)."
a) N(1) = (1/sqrt(10)) <3,1>
b) N(1) = (-1/sqrt(10)) <3,1>
c) N(1) = (1/sqrt(10)) <1,-3>
d) N(1) = (1/sqrt(10)) <-1,3>
My answer is either c) or d), and I'm wondering which one is correct. If you were to draw a graph of <t^3, t> and then try to get a perpendicular vector to <3,1> then answer c) and d) make sense. However my question is whether I need to point away from the curve, or into it? If away then c) and if into then d). Is my thought process correct? If not what am I not seeing.
Feb 13th 2011, 04:14 AM
The normal vector to a curve points inward. Think of the situation with a circle. The normal vector points toward the center of a circle. More generally, it points toward the "center of curvature" of a curve, the center of a circle that most closely approximates the curve.