Finding the displacement thru position vectors

[pratjoehahn]

Homework Statement

A particle is displaced by 10m along a direction joining 2 points having coordinates A(2,3,4) and B(-4,-5,3).Find the displacement vector if the time of the motion is 2.5 seconds.Find avg. velocity of this particle.

Homework Equations

vector AB = (x₂-x₁)i + (y₂-y₁)j +(z₂-z₁)k

The Attempt at a Solution

using the above equation I got the position vectors but I don't know how to do anything after that...I can maybe but displacement is already given(10m) so why does it tell to find the displacement again.
Behind the book I checked the answers and got this 10[(-6i -8j -k)/sqrt(101)].

 

[jhae2.718]

It wants the displacement vector along the direction of the vector from A to B.

This vector will have a magnitude of 10 m, and will be in the direction of the vector from A to B.

 

[pratjoehahn]

but the answer still bugs me ... I know 10 is the magnitude but what is (-6i -8j -k)/sqrt(101) ?

 

[SteamKing]

The displacement vector of 10m has the same direction as the vector (B-A) but it is not identical to (B-A). Hint: think unit vector multiplied by a magnitude.

 

[rwisz]

I would first clarify the question with the person who gave the assignment. It seems that the question is asking for the displacement vector between points A and B, which is already given as 10m. However, the answer provided in the book is asking for the displacement vector in a specific form (with the unit vector and square root). I would ask for clarification on whether this specific form is necessary for the answer or if the 10m value is sufficient.

Furthermore, I would also ask for clarification on what is meant by "time of the motion is 2.5 seconds". Is this referring to the total time of the particle's motion or the time it took to travel from point A to point B? This information is necessary in order to calculate the average velocity of the particle.

Once the question is clarified, I would use the given coordinates to calculate the displacement vector using the equation provided. Then, if necessary, I would convert the displacement vector into the specific form given in the answer. To find the average velocity, I would divide the displacement vector by the time of motion, as velocity is defined as displacement over time.