Calculus applications-vectors, determinant, dot product...etc

Question

amtran_bus · Answer

Given the following system of vectors:
1. Define vector equations for U and V
2. FInd the determinant of this system in R^2
3. Find the dot product of these vectors
4. Determine the angle between the vectors, given that     |u| |v| cos(theta) =u*v

|dw:1360347756320:dw|

amtran_bus · Answer

The (2,2) is the first equation for that line as (1,2) is for the first line.

amtran_bus · Answer

Ok, so I need an I, J, and K value for these vectors.  However, I don't think I will get a k from this linear display. This should give me an equation for each?

anonymous · Answer

sure, if you do it like that. I usually use the vector geometric definition:

$$\Huge \vec{AB}=0B-0A $$

amtran_bus · Answer

|dw:1360348090159:dw|
Sorry, did not label.

How would you write the equation for u?  Do I combine the 2 x and y values given?

anonymous · Answer

$$\Large \vec{AB}=\vec{U}=(3,7)-(1,2)=(2,5) $$ You basically subtract the x from the x and the y from the y (-:, as you considered

amtran_bus · Answer

Good!  Ok, so the matrix is like

I    J
2  5
4  1



???

anonymous · Answer

Usually the vector notation looks a bit more elegant *grins*; But I guess you know how you would write it out more rigorously.

amtran_bus · Answer

Oh yea, don't worry!

amtran_bus · Answer

So equation for u= 2i+5j
and v=4i+1j, correct?

(besides notation lol)

anonymous · Answer

Hmm, someone else needs to help you there, I haven't seen such a notation before, if they would ask me for the determinant of these two vectors I would write it out like:

$$\left[\begin{matrix}2 & 4\ 5& 1\end{matrix}\right]$$ and compute the determinant.

anonymous · Answer

yes you're right about that, that's the notation for the vectors in algebraic form.