1. ## unidirection Vectors

Hi,

Assume that I've vector u = [7 6 -3]

and I've vector v in the same direction as u with initial point A= (2,-1,4)

so is it enough to say that v=K[7 6 -3]

or I've to say that B= A + v = (2+7k,6k-1, 4-3k)

Thanks

2. ## Re: unidirection Vectors

Originally Posted by ahmedzoro10
Assume that I've vector u = [7 6 -3]
and I've vector v in the same direction as u with initial point A= (2,-1,4)
so is it enough to say that v=K[7 6 -3]
A + v = (2+7k,6k-1, 4-3k)
First you should say that in order to have the same direction it must be that $k>0$.

The equation in blue is a line through A with direction u.

So I am not really sure what you need.

3. ## Re: unidirection Vectors

Originally Posted by Plato
First you should say that in order to have the same direction it must be that $k>0$.

The equation in blue is a line through A with direction u.

So I am not really sure what you need.
I want to know what vector v which is the same direction of u and has A as initial point

if i only wrote v=k[7 6 -3] when k>0 so what the need for mentioning A!

4. ## Re: unidirection Vectors

Originally Posted by ahmedzoro10
I want to know what vector v which is the same direction of u and has A as initial point
if i only wrote v=k[7 6 -3] when k>0 so what the need for mentioning A!
Frankly I do not know. Neither do I know what your text/instructor has to say about it.

Generally speaking, a vector is an equivalence class of 'objects' that have the same length and same direction. As such, the notion of initial point is mute. By that is meant, starting at any point 'moving off' in the same direction with the same length gives the same vector.

Vectors are parallel if they are non-zero multiples of each other.
They have the same direction if the multiple is positive.