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Unformatted text preview: PRACTICE PROBLEMS FOR MIDTERM Note that no book, lecture notes or calculators are allowed during the midterm. The actual midterm problems will be slight variation from problems here. Note that we denote a vector by a letter in boldface, such as a , b , v , i , j , k . Question 1. Let a = i- k + 2 j , b = k- j . (1) Compute a · b , a × b , a · ( a × b ) and a × ( a × b ) ; (2) The angle θ between a and b , the vector projection of b onto a and the scalar projection of b onto a ; (3) Find the vector / parametric/ symmetric equations of the straight line l which goes through the origin and parallel to a ; Find the distance from the point P = (0 ,- 1 , 1) to the line l 1 ; (4) Find the equation of the plane p 1 which goes through the point P and perpendic- ular to the vector a . (5) Given a vector function r ( t ) = ( te- t +1) i +cos( πt ) j +ln(3 t +1) k , find the derivative r ( t ) of the vector function r ( t ) and find the vector (or parametric, or symmetric ) equations of the tangent line...
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This note was uploaded on 02/27/2011 for the course MATH 101 taught by Professor Y during the Spring '11 term at Columbia College.
- Spring '11