00:01
For this problem, we are asked to determine if the following statement is true or false and to give reasons for our answer.
00:08
The statement here is that if the vector r equals the vector r is a function of s and t parameterizes the upper hemisphere, x squared plus y squared plus z squared equals 1, where z does not equal, or excuse me, z is greater than or equal to 0, then r equals negative vector r.
00:30
R of s and t parameterizes the lower hemisphere, x squared plus y squared plus z squared equals 1, for z less than or equal to 1.
00:41
So to begin, based on our initial statement, i'll sort of split this apart into two different statements.
00:49
Our first statement, one, and then our second statement, two.
00:56
For statement one, if we have that r fully parameterizes the upper hemisphere, then we would need to have that, however r is defined, it would need to be covering negative, let's see here, it would need to be covering negative 1 is less than or equal to x is less than or equal to 1...