Calculating unit vector for velocity

[andykol]

Hello,
I am trying to calculate unit vector for velocity (vel= (U*Unit vector)/unit vector). But if I consider calculation by angle change e.g. unit vector= cos(theta) at certain angle velocity becomes infinity.
Please inform me how I can take care of this problem.
Thanks in advance.

 

[junglebeast]

vel= (U*Unit vector)/unit vector).

This equation makes no sense.

unit vector= cos(theta)

This equation makes even less sense...as cos(theta) is a scalar not a vector.

Typically you make unit vectors by normalizing them, which means to divide by the length.

 

[John Creighto]

The unit vector for velocity would be:
$$U=\left(\frac{V_x}{|V|},\frac{V_y}{|V|},\frac{V_z}{|V|}\right)$$

where the magnitude of the velocity vector is given by:

$$|V|=sqrt(V_x^2+V_y^2+V_z^2)$$

and

$$V_x$$,$$V_y$$,$$V_z$$, are the $$x$$, $$y$$, and $$z$$ components of the velocity vector respectively.

However, without more information on the original problem I'm not sure if this is what you want.

 

[andykol]

Thanks for reply.
I am trying to multiply velocity with unit vector to transfer velocity without calculating at perticular location. Please see attached picture. Please tell me if I m using right equation and its values.

John,
I need to use following equation to calculate velocity for 2D?

$$Unit vector=\left(\frac{U_x}{|U|}+\frac{U_y}{|U|}\right)$$

$$|U|=sqrt(U_x^2+U_y^2)$$

Then I can calculate U' by (U(x,y)*Unit vector(x,y))/unit vector(x,y)

 

[John Creighto]

Thanks for reply.
I am trying to multiply velocity with unit vector to transfer velocity without calculating at perticular location. Please see attached picture. Please tell me if I m using right equation and its values.

John,
I need to use following equation to calculate velocity for 2D?

$$Unit vector=\left(\frac{U_x}{|U|}+\frac{U_y}{|U|}\right)$$

$$|U|=sqrt(U_x^2+U_y^2)$$

Then I can calculate U' by (U(x,y)*Unit vector(x,y))/unit vector(x,y)

I think what you want is the dot product. The dot product will give you the component of the velocity in the direction of the unit vector.

For a unit vector u the projection of V on U is given by:

$$Proj_UV=U\cdot V=UxVx+UyVy+UzVz$$

 

[andykol]

means-
If we consider one direction like picture I have attached in last post.
U- Velocity(known)
U'-Velocity(unknown)
Uv-Velocity Vector

Then if I am transferring velocity value

U'=U.Uv

Where $$U_v=\left(\frac{U}{|U|}\right )$$

But this becomes U'=U. I think this is wrong as location of velocity changes.

 

[John Creighto]

means-
If we consider one direction like picture I have attached in last post.
U- Velocity(known)
U'-Velocity(unknown)
Uv-Velocity Vector

Then if I am transferring velocity value

U'=U.Uv

Where $$U_v=\left(\frac{U}{|U|}\right )$$

But this becomes U'=U. I think this is wrong as location of velocity changes.

To make your posts more clear, use subscripts for components of vectors. Now reread my last two posts. As far as I understand your problem, you are trying to find the component of the velocity in the direction of the unit vector. This is not the same thing as finding the velocity.

 

[andykol]

Thank you John. This helped a lot.