math 265 - plane.) 3. Show that the parametric curve ( x (...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 265 (Butler) Practice Midterm I – A Try to answer the following questions without the use of book, notes or calculator. Time yourself and try to finish the test in less than 50 minutes. 1. A particle moves through three dimensional space with velocity v ( t ) = h sec 2 t, 2 sec t tan t, tan 2 t i . At time t = 0 the particle is at h 0 , 1 , 2 i , find the position function of the particle for - π/ 4 t π/ 4. 2. Find the points on the plane x +2 y = 5+3 z which is closest to the point (4 , 4 , - 7). (Hint: you do not need calculus to find the answer. Useful hint: the line that connects the point (4 , 4 , - 7) to the nearest point on the plane will be perpendicular to the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: plane.) 3. Show that the parametric curve ( x ( t ) ,y ( t ) ,z ( t )) = (1-sin(2 t ) , 2(sin t + cos t ) , cos(2 t )) lies on a sphere centered at the origin. Also, nd the radius of the sphere. 4. Find the area of the quadrilateral in the plane with vertices located at (3,1), (7,3), (4,4) and (0,3) using vector techniques. 5. Find the cumulative length function s ( t ) (starting from a = 1) of the parametric curve h ln t, 2 t, 1 2 t 2 i ....
View Full Document

Ask a homework question - tutors are online