MHB Help with Vector Questions in a Cartesian Coordinate System

[paulmdrdo1]

I'm not sure if it is the right place to post my questions to. please let me know if this should be somewhere else.

1. let each of the vectors

$A=5a_x-a_y+3a_z$
$B=-2a_x+2_ay+4a_z$
$C=3a_y-4a_z$

extend outward from the origin of the cartesian coordinate system to points A,B, And C respectively. find a unit vector directed from point A toward

a.) Origin b.) point B c.) Equidistant from B and C on the line BC. d.) Find the length of the perimeter of the triangle.

2. The vector $R_{ab}$ extends from A(1,2,3) to B. if the length of $R_{ab}$ is 10 units and its direction is given by $a=0.6a_x+0.64a_y+0.48a_z$ Find the coordinates of B.I already answered letter B in prob 1. but got stuck on the remaining items.

please help. thanks!

 

[Prove It]

First of all, get vectors going in the right direction, then scale them to get the right lengths.

 

[paulmdrdo1]

what do you mean? the vectors already have directions.

 

[DavidCampen]

I'm not sure if it is the right place to post my questions to. please let me know if this should be somewhere else.

1. let each of the vectors

$A=5a_x-a_y+3a_z$
$B=-2a_x+2_ay+4a_z$
$C=3a_y-4a_z$

extend outward from the origin of the cartesian coordinate system to points A,B, And C respectively. find a unit vector directed from point A toward

a.) Origin b.) point B c.) Equidistant from B and C on the line BC. d.) Find the length of the perimeter of the triangle.

To convert each of the given vectors to unit vectors you would divide each vector by its length.

When they ask for a unit vector from point A to the origin it is hard to know what is wanted since the line of unit length from point A to origin is a directed line segment not a vector. Do they want you to perform a translation of axes so that point A becomes the origin or do they want you to specify the coordinates of a directed line segment of unit length from A towards the origin?

Euclidean vector - Wikipedia, the free encyclopedia

As an informational object, the vector is not as informative as a directed line segment (an ordered list of two points [ A , B ]) but rather expresses the displacement, or vector offset (change in location), A --> B.

 

[Evgeny.Makarov]

When they ask for a unit vector from point A to the origin it is hard to know what is wanted since the line of unit length from point A to origin is a directed line segment not a vector. Do they want you to perform a translation of axes so that point A becomes the origin or do they want you to specify the coordinates of a directed line segment of unit length from A towards the origin?

Let's not overthink this. An ordered pair of points determines a vector.

 

[DavidCampen]

Let's not overthink this. An ordered pair of points determines a vector.

So you are saying that the answer would be to specify coordinates for 2 points - one being point A and the other being a point a unit length along the line segment from point A to the origin? Wouldn't this be a directed line segment, not a vector?

 

[Evgeny.Makarov]

So you are saying that the answer would be to specify coordinates for 2 points - one being point A and the other being a point a unit length along the line segment from point A to the origin?

No, the problem statement says, "Find a unit vector directed from point A toward a.) origin, b.) point B, ...". I believe one needs to subtract the coordinates of A from the coordinates of the origin (or B) to get the coordinates of the vector $v$ that points from A to the origin (or B), and then divide those coordinates by the length of $v$ to get the coordinates of the unit vector.

 

[DavidCampen]

No, the problem statement says, "Find a unit vector directed from point A toward a.) origin, b.) point B, ...". I believe one needs to subtract the coordinates of A from the coordinates of the origin (or B) to get the coordinates of the vector $v$ that points from A to the origin (or B), and then divide those coordinates by the length of $v$ to get the coordinates of the unit vector.

So that would give us the negative of the unit vector for A but this is directed from the origin away from point A; which is not what the question asks, but yes, it is probably the intended "correct" answer. This is the reason I detest these problems that are worded imprecisely because forcing you to guess at what answer the professor will consider "correct" is the only way to give the problem any difficulty - and then the difficulty is not in the math. If the professor wanted you to supply the negative of the unit vector then that is what should have been asked for.

Now, the problem of finding the number of unique sets of n objects that can be formed by selecting 0 or more of each of n symbols; I thought that that was a fun problem.