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.