#$&*
Mth 277
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
** **
query_10_1
Question: Find the domain of F(t) X G(t) when F(t) = t^2 i - (t+2)j + (t-1)k and G(t) = (1/(t+2))i + (t-5)j + sqrt(t) k.
** **
This is the question I do not understand. I understand domain and all. I was just trying to figure out what we do about the cross product and such and since it has the i,j,k components in it. Do we just set it up like a regular cross product and we take the domain of the result. How do we plug in and what would be the solution? I would really just appreciate a solution to this to help me understand.
@&
The domain of F X G includes all the points that are in the domain of both functions.
There are not restrictions on the domain of F, and the only restrictions on the domain of G are that t cannot be negative and t cannot be equal to 2.
So the domain of the cross product is
{t | t >=0 and t <> 2}.
Note that <> indicates that t cannot equal 2.
*@
#$&*
Mth 277
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
** **
Find a vector function F whose graph is the curve given by the equation x/5 = (y-3)/6 = (z+2)/4.
** **
I understand a vector function is a function of one variable. I was just wondering how we simplify this into the correct answer and form that you would be looking for on such an item as a test. I was a bit confused and the book did not help me understand that well. If you could direct me to a sample problem like this it would be very helpful.
** **
Thank you so much for all your assistance and help in understand the course material.
@&
This is the symmetric equation of a straight line.
It can be converted to a set of parametric equations in any variable you might want to choose, other than x, y or z. The usual default choice is t.
x/5 = (y-3)/6 = (z+2)/4 means that all three expressions are equal. If we use t for the quantity to which they are equal we get the equations
x/5 = (y-3)/6 = (z+2)/4 = t
so that
x/5 = t
(y-3)/6 = t
(z+2)/4 = t.
It follows that
x = 5 t
y = 6 t + 3
z = 4 t - 2.
Thus the vector function
F(t) = x(t) i + y(t) j + z(t) k = 5 t i + (6t+3) j + (4t - 2) k, -infinity < t < infinity
where F, i, j and k represent vectors (it's not practical to boldface them using a text editor, but that is how they should be regarded).
represents the same locus of points as the original equation
x/5 = (y-3)/6 = (z+2)/4
*@
@&
See also the notes on the DVD's (and/or as posted from the assignments page).
*@
#$&*
Mth 277
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Star on Query Problems
** **
** **
On some of the query problems on the Assignments tab, there are stars beside them, I was wondering if this indicates something or means anything special. Does this maybe indicate to pay special attention to these problems?
** **
@&
Those stars are mostly there as editing aids. You can ignore them.
*@