Hi, I have question and I don’t know how to realize it. Let’s say I have 4 Vector3 and I want to increase each of them on the zaxis by 100 and at the same time keep the angle of these vectors (as in the picture). In other words, I need the vector to be greater along the zaxis by 100 and always parallel to the initial vector. I will be glad for any advice.
I’m not sure I understand the question.

THREE.Vector3
is a position vector, thus its coordinates define its size (direction and length) only, and there is no data about where in the plane is the vector – positionvectors are by definition assumed to start from (0,0,0). 
Your image features another type of vector, some call it directed segment. It has a beginning and end, thus in Three.js such vectors are represented by two
THREE.Vector3
. 
In Three.js there is a third type of vector, called direction, used for rays and raycasting. It is defined by two THREE.Vector3; the first one is the position of the beginning, and the second one is a unit position vector relative to the beginning.
The answer to your question strongly depends on what type of vector you do mean:

Position vectors can change their Z coordinate and keep the same direction by uniform scaling. For example:
(x,y,z) → (kx,ky,kz), where k = (z+100)/z
Note: This is not available for all vectors, for example, the operation is undefined for (0,0,0); and it will flip the direction for (0,0,1). 
The transformation of directed segments is done by the addition to both THREE.Vector3, thus translating the vector without rotation. For example:
[(x_{1},y_{1},z_{1}), (x_{2},y_{2},z_{2})] → [(x_{1},y_{1},z_{1}+100), (x_{2},y_{2},z_{2}+100)]
Note: This is available for all directed segments. 
The transformation of directions is done by the addition to the first THREE.Vector3. For example:
[(x,y,z), (u_{x},u_{y},u_{z})] → [(x,y,z+100), (u_{x},u_{y},u_{z})]
Note: This is available for all directions.