| On 8/26/99, nelsonca asks about Q15 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
I thought since it said the value of t and the equation had a minus sign in front of t that that would make it +.4. Response: You are correct. I missed my own problem (this won't be the last time). I have changed the key to give the correct answer. Thank you. |
| On 8/26/99, nelsonca asks about Q19 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
I'm lost on this one. Response: To get the angle the v vector makes with the x-axis, calculate arccos( (v dot i)/|v|), where i is the vector [1,0,0]. Similarly for the other two angles. |
| On 8/26/99, nelsonca asks about Q20 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
but you could end up with 1+1+1 can't you? Response: If so, then there would be a vector in R^3 which makes an angle of 0 or 180 degrees with each coordinate axes. |
| On 8/28/99, colleter asks about Q10 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
The correct answer said that there is a unique value of t for each value of s, isn't it also true that there would be a unique value of s for each value of t as well? Response: Yes, it could be stated that way also. |
| On 8/28/99, colleter asks about Q11 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
Will we always round to 4 significant figures in the future for this class? Response: No. |
| On 8/28/99, colleter asks about Q12 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
I think that this is a tricky question in some sense because in the question there is no reference to what dimenison U,V, and W are. In 2-D the answer would be true, but in 3-D or higher the answer could be true or false. Response: Important point. Since no reference was made to the dimension of the vectors, and the statement is false for 2 dimensional vectors, the statement is false. In order for a statement to be true, it must be true in all instances. |
| On 8/28/99, colleter asks about Q19 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
I knew how to find these angles from a previous course that I have had, but what is the books approach? I had trouble making the connection, but I could be overlooking something. Response: Use the cosine formula on page 15. |
| On 8/28/99, colleter asks about Q8 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
I calculated this value on my calculator and got the right answer, but should I be able to figure out the answer without using the arccosine function to find the angle? Response: That would be the simplest way, unless it were an angle like 90, 60, 45, or 30 degrees. |
| On 8/28/99, colleter asks about Q9 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31):
This was a easy and fun one equation, one unknown if you realize that U perpendicular with A means U dot A = 0. |
| On 8/31/99, claybomi asks about Q10 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31 or Sept 2):
I don't understand how there can be a unique value for one and not the other. Response: Write down the equation which expresses the fact that [s,t,5] and [7,3,-4] are perpendicular. Solve the equation for t. Then for each value of s this equation will give you the unique value for t. It goes the other way too: for each value of t there is a unique value for s. But there are not unique values for both s and t. |
| On 8/31/99, claybomi asks about Q8 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31 or Sept 2):
For this one I got 91 degrees. I was told if I answered with neither answer then it would be wrong. Response: Recalculate this one, Michael. You should get 83.135 degrees. |
| On 9/1/99, belhajse asks about Q12 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31 or Sept 2):
I think that this one should be True! Response: We discussed this in class. Somebody gave the example of U = [0,0,1], V=[1,0,0] and W=[0,1,0] to show the statement is not true. See above 8/28/99, colleter asks about Q12 also. |
| On 9/1/99, belhajse asks about Q13 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31 or Sept 2):
And this one should be also true! Response: Let U = [1,0] and V=[0,2]. Then U+V = [1,2] and U-V = [1,-2] are not perpendicular, since [1,2] dot [1,-2] = -3, not 0. |
| On 9/1/99, beltja asks about Q13 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31 or Sept 2):
I thaught this was saying that u+v & u-v were perp to u & to v. Not to each other. Response: Read it again more carefully. |
| On 9/1/99, beltja asks about Q15 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31 or Sept 2):
I just got tricked by this one, I knew it was .4 but for some reason was thinking of -t. Response: So did I (and it was my question). See above 8/26/99, nelsonca asks about Q15. I changed the key to the correct answer at that time. |
| On 9/1/99, beltja asks about Q20 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31 or Sept 2):
How come they can't be greater than? Response: Discussed in class 9/2. Let [x,y,z] be the vector. Use the cosine formula on page 15 to get cos^2(alpha) + cos^2(beta) + cos^2(lambda) = x^2/(x^2+y^2+z^2) + ... = 1. |
| On 9/1/99, beltja asks about Q7 of MA322-005,Section
1.1 to 1.2 (Complete by Aug 31 or Sept 2):
When I solved for x on this one I got X = (2/3)A - (1/3)/B Response: You have a sign error. AX = X-A, XB = B-X, and 2(X-A) = B-X implies X = (2/3)A + (1/3)B. |