126_Au07_Sol2

126_Au07_Sol2 - Math 126 Sections C and D Fall 2007...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 126, Sections C and D, Fall 2007, Solutions to Midterm II 1. Consider the vector function r ( t ) = < 4 t + 1 , t 2- 3 t, cos( t ) > . (a) Find the unit tangent vector T at (1 , , 1). (4 points) T (0) = r prime (0) | r prime (0) | r prime ( t ) = < 4 , 2 t- 3 ,- sin( t ) > r prime (0) = < 4 ,- 3 , > T (0) = < 4 ,- 3 , > | < 4 ,- 3 , > | = < 4 ,- 3 , > √ 16 + 9 + 0 = < 4 5 ,- 3 5 , > (b) Find the normal plane to the curve at (1 , , 1). (3 points) 4 5 ( x- 1)- 3 5 ( y- 0) + 0( z- 1) = 0 4 5 ( x- 1)- 3 5 y = 0 (c) Find the curvature at (1 , , 1). (4 points) κ = | r prime × r primeprime | | r prime | 3 So we need r primeprime ( t ) = < , 2 ,- cos( t ) > r primeprime (0) = < , 2 ,- 1 > r prime × r primeprime = < 3 , 4 , 8 > So κ = √ 9 + 16 + 64 5 3 = √ 89 125 1 2. Consider the two lines r 1 ( t ) = < 2 t- 1 , 3 t, 5 t- 2 > and r 2 ( s ) = < 4 s- 1 , 6 s + 1 , 2 s + 2 > . (a) Show that they are skew. That is, show that they do not intersect, and that they are not parallel....
View Full Document

{[ snackBarMessage ]}

Page1 / 4

126_Au07_Sol2 - Math 126 Sections C and D Fall 2007...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online