Key to Practice Midterm II

Problem 1

  1. True,  Since uxv is perpendicular to u, its dot product with u is zero.

  2. False,  the curves could go through the origin at different times

  3. False,  there is a k with k<a,b,c> = <4,5,3> hence,  
    4a + 5b + 3c = k<a,b,c>.<a,b,c> = k(a2 + b2 + c2) is not zero.

 

Problem 2

-3x - 11y + 21z =5

Problem 3

qz = r2 + z2 

Problem 4

Problem 5

A.  x = -1 + 2cos[-(t-p)]

B.  y = 4 + 2sin[-(t-p)]

Problem 6

cos-1(-3/sqrt58)

Problem 7
y = x2 + z2 

Problem 8

the slope for the second curve is 

(cfcosq +cf'sinq )/(-cfsinq  + cf'cosq )  =  (fcosq +f'sinq )/(-fsinq  + f'cosq )

which is the slope for the first curve.

Problem 9

F = -1500i + 10,000j + 5000(sqrt2 - 2)k