TheTraveler
New member
- Joined
- May 7, 2022
- Messages
- 4
Hi all!
I was studying a demonstration about vectors projections and it starts with this image:
The demonstration starts solving by v|| and it says that:
[math]\mathbf{v}_\| = \mathbf{n}(\| \mathbf{v}_\|\| / \| \mathbf{n}\|)[/math]
and this is the unclear step.
I tried to unroll this step (which is not explained in the demonstration) and I thought about using the dot product:
[math]\mathbf{n} \cdot \mathbf{v}_\| = \|\mathbf{n}\| * \|\mathbf{v}_\|\| * \cos\theta[/math]
and, because the two vectors are parallels, the angle is 0 and the cosine is 1, so it results:
[math]\mathbf{n} \cdot \mathbf{v}_\| = \|\mathbf{n}\| * \|\mathbf{v}_\|\|[/math]
but from here on out I don't really understand how to proceed to obtain the first step. Any suggestion? I know it's probably a stupid thing but I cannot figure it out ?
I was studying a demonstration about vectors projections and it starts with this image:
The demonstration starts solving by v|| and it says that:
[math]\mathbf{v}_\| = \mathbf{n}(\| \mathbf{v}_\|\| / \| \mathbf{n}\|)[/math]
and this is the unclear step.
I tried to unroll this step (which is not explained in the demonstration) and I thought about using the dot product:
[math]\mathbf{n} \cdot \mathbf{v}_\| = \|\mathbf{n}\| * \|\mathbf{v}_\|\| * \cos\theta[/math]
and, because the two vectors are parallels, the angle is 0 and the cosine is 1, so it results:
[math]\mathbf{n} \cdot \mathbf{v}_\| = \|\mathbf{n}\| * \|\mathbf{v}_\|\|[/math]
but from here on out I don't really understand how to proceed to obtain the first step. Any suggestion? I know it's probably a stupid thing but I cannot figure it out ?