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C) For the points A( 5,6) and B( 8,10determine the position vector AB...

Question

C) For the points A( 5,6) and B( 8,10determine the position vector AB

c) For the points A( 5,6 ) and B( 8,10 determine the position vector AB



Answers

Equal vectors For the points $A(3,4), B(6,10)$ $C(a+2, b+5),$ and $D(b+4, a-2),$ find the values of $a$ and $b$ such that $\overrightarrow{A B}=\overrightarrow{C D}$.

In this problem, we have been given two points A&B. Now the coordinates of A are given to be the coordinates five, coma be coma C. And the coordinates of the point. We are given to e minus 38 Now it is said that both of these points are located at the same point in our three. We need to use this information to determine the values of A. B and C. Now A and B are actually the same point because they are located at the same point does the coordinates will be equal? So that means that five Bc will be the same as a minus 38 So we can equate the corresponding coordinates. So the host coordinate, which will be the X coordinate that will fight. This will be equal to eat the Y coordinate B will be equal to the y coordinate of the second point, which is minus three. Similarly, we equate the z coordinates to get C is equal to eight. Hence the values are a is equal to five, B is equal to -3 and C is equal to eight. Now, in the next problem we need to write the vector corresponding to E. Now first of all know that the coordinates of the point. We are five comma comma C. So this will be the point A five minus 38 Because B is -3 and C is eight, and hence the vector corresponding to E will be the victor you and the component form will be the same as the coordinates at this point. So the component form will be five minus 38 hence five minus 38 will be the sector, which corresponds to oh he.

In this video, we're going to go through a series of problems that share a lot of similarities. We're talking about vectors in the plane. So if we have the points that are given, we want to find position vectors. So a good way to do this is to take two points. As an example, let's say we have A is um to three and be Is 6 -4. It doesn't matter what it is. It's random. We need to find a position vector which will call V. It's going to equal the components subtracted. So if we're going from A to B we're going to take B X component minus A X components will be six minus two inches four and then we'll have negative four minus three which is -7. So that would be the um position doctor. We can also consider other points and we could find the values such that like in 62 such that A. B equals C. D. Well forgive another values. We just need to find A B. Once we find maybe we can find CD which were called back to you and then we just set the individual components. Let's say this gives us X. This gives us why we said the individual components equal to the V components. And then we just solved for it algebraic lee fairly simple to do. Um And that is going to be I'm our answers to those following problems

Peeing cute, located three Want and someone to, and we're off to find position directors that are equal into P. Q and Q P. So let's find a vector p kill first. Let's do it. So this is our director. It's not really state, but this is our vector p. Q. So to find inspector components, we just need to find the changing X, Delta X, and we're changing away. We can do this out directly, but it's easier for here to, like just count. So it's 123 and four, so Delta X is equal to four. I'm on Delta Y is just one. So our rector pick you has to falling components four and one. So remember that any back through dot has the same length, which means they have the same man, same component, and they point to the same direction. Ari Cool. And so R. P Cube, is it going to its position factor double started origin. So our position factor that will started the origin is equivalent to P Q. And it's equal to 41 seamer alertly QP points to a different direction. All do it in a different color. So this is our acute peak. It points to a different direction, being that changing white and treating X are the same. So our Q P starts a que pointing at P, meaning it has the same Children accent in you. Why? But it has a different direction, so it will be the opposite off peak ill. So a negative P. Q. On its position factor. Let's a position, but there you will illegal to this, and it will be needed off for one, so it's native for native one.

But this Pierpoint and we are us to find position directors equal into each of these factors provided and just to recall director Sorry, Google. And if they have the same direction and same magnitude, which means they're components need to be a gobbling. It doesn't matter of our day store. It's just they need to have, um, equivalent components, so less like you better and be so it starts from point A and goes to Point B on just to recall components are a cola changing X on changing white. So this will equal to point A is native tune zero bees six and 16. So changing acts real equal to six minus negative, too six minus made it to and then chignon. Why will equal to 16 minus zero and this is equal to six was too eight and 16 and this is our position back there. Same for a C. He starts at point A and goes to Point C. So all we do is changing accent changing white. So it's one minus negative, too, and then four minus zero, which is equal to one plus two three. And for and then we have point A to f so it will be three. Route to mine is rude to and then native for route to mine is rude to So this is equal to to root two and then negative. Why route to are for a C today? So it will be changing x again. So life minus one on then changing white We chase for minus four which is equal to before and that zero So the letters that we found in here part all equal to the position fighters.


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