Calc III, Vector trouble, help would be great

[mr_coffee]

Hello everyone I have a few problems I ran into doing my homework. Its on vectors. Any help would be great! The professor didn't give me any ones i could check in the back of the book and his office hours are very bad for me, sorry for all the questions!

This one is probably really simple, i don't understand how I'm suppose to write it.
4. Write each combination of vectors as a single vectory.
(c) QS - PS; (d) RS + SP + PQ; //i can't draw vector notation, but there should be an arrow on top of each group of letters, like QS.

31. A woman walksdue west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 22 mi/h. Find the speed and direction of the woman reltive to the surface of the water. I found the speed by just using sqrt(3^2 + 22^2) = 22.2 mi/h. But I'm confused on how I'm suppose to find the direction. THe book has an answer of: North 8 degrees West.

34. The tension T at each end of the chain has a magnitude 25N. What is the weight of the chain. The picture looks like it has a triangle on each side of the bank, forming a 37 degree angle. The trinagle is tension of course. So i figured the X compoents would cross out and u'd be left with the Y compoents in the +Y direction, so i just added those 2 vectors up and got 30 lb, does that sound like the right procedure?

40. If r = <x,y>, r1 = <x1,y1>, and r2 = <x2,y2>, describe the set of all points (x,y) such that |r - r1| + |r - r2| = k, where k > |r1-r2|
I'm completely lost on this one.

43. Use vectors to prove that the line joining the midpoints of two sides of a traingle is parallel to the third side and half its length. I'm also confused on how to do this one.

Thanks!

 

[teclo]

4.
i'm not sure what you're looking for here. do you have coordinates for Q, S, P, and R? remember that a vector in $$R^3$$ is

$$\vec{A} = \left( \begin{array}{cc} A_x \\ A_y\\ A_z \end{array} \right)$$

so, perhaps you should just break the vectors up into components, carry out the operations, and report them in cartesian coordinates, or perhaps in unit vector components? i don't know, just some ideas.

31.
assuming the surface of the water is the inertial reference frame, this isn't so tough. add the two vectors, find the magnitude. you got that far -- now, think of a geometric description of what you've done. you've added two vectors and now have a resulting vector in the second quadrant. you've got a triangle -- can you figure out the angle with that?

34.
sounds reasonable. i can't really imagine your picture at this ungodly hour -- i do suspect that you've done it correctly. for these you add up all the vectors ala their separate components.

40.
yah, that makes two of us

43.
i'm not sure on what the preferred approach to this would be either. let's say you've got triangle ABC. now, can you perhaps come up with cartesian coordinates for the midpoints of A and B? to get the vector for the new triangle produced, you'd just have to subtract one from the other, right?

so, I'm sure you can see that however you do this, it will be parallel to C. what kind of vector operations depend on the angle between two vectors? (hint: *dot product*, cross product.


i haven't worked any of these out, but perhaps i can at least shed some perspective on them? I'm in calc 3 now, so I'm no master at this business.

cheers

 

[JoAuSc]

40. If r = <x,y>, r1 = <x1,y1>, and r2 = <x2,y2>, describe the set of all points (x,y) such that |r - r1| + |r - r2| = k, where k > |r1-r2|
I'm completely lost on this one.

Draw vectors r1, r2, and r all coming from the same point. Then draw r-r1 and r-r2. Picture a string running from point r1 through the origin to point r2. Because |r-r1| + |r-r2| = k, a constant, the string's length cannot change. Now, what shape would you draw if you were to draw with your pen through all points such that your pen was pushing out on the string, stretching it taught?

 

[lightgrav]

4. The vector from Q to S , minus the vector from P to S ?
the negative of PS_vector is SP_vector.
So, what is QS + SP ?

Surely you're not expecting to get through calc 3
without drawing diagrams?!