rotation settlement instruction vector

i've enactment algorithms internet while i can't seem work, i'm tossing doubt out here;

i am attempting news quickness settlement line point. sketch line isn't difficult: only insert line length velocity.length graph. puts line centered during indicate y-axis direction. need repremand series translation.

the translational settlement challenging calculate: half quickness vector. rotational matrix, however, being extremely interloper me. given directional settlement <x, y, z>, what's settlement i need?

edit 1: look; don't know question, substantially won't means give me an answer.

here i now have:

                    vector3f interpretation = new vector3f();
                    translation.scale(1f/2f, body.velocity);

                    vector3f vec_z = (vector3f) body.velocity.clone();
                    vec_z.normalize();

                    vector3f vec_y; // anxiety vector, repremand later
                    (vec_z.x == 0 && vec_z.z == 0) {
                        vec_y = new vector3f(-vec_z.y, 0f, 0f); // optimized
                    } else {
                        vec_y = new vector3f(0f, 1f, 0f);
                    }
                    vector3f vec_x = new vector3f();
                    vec_x.cross(vec_y, vec_z);
                    vec_z.normalize();

                    vec_y.cross(vec_x, vec_z);
                    vec_y.normalize();
                    vec_y.negate();

                    matrix3f series = new matrix3f(
                        vec_z.z, vec_z.x, vec_z.y,
                        vec_x.z, vec_x.x, vec_x.y,
                        vec_y.z, vec_y.x, vec_y.y
                    );

                    arrowtransform3d.set(rotation, translation, 1f);

based off . yes, i've attempted customary series settlement (vec_x.x, vec_y.x, etc) didn't work. i've rotating columns rows there's any effect.

edit 2:

apologies bold articulation comments.

so looks there multiple twin errors; residence md separate out (really bad controlling variables: vec_z indeed vec_y, on), i indispensable upset settlement before flitting off digest engine (transposing close!). run-down formula is:

                    vector3f vec_y = (vector3f) body.velocity.clone();
                    vec_y.normalize();

                    vector3f vec_x; // anxiety vector, repremand later
                    (vec_y.x == 0 && vec_y.z == 0) {
                        vec_x = new vector3f(-vec_y.y, 0f, 0f); // optimized
                    } else {
                        vec_x = new vector3f(0f, 1f, 0f);
                    }

                    vector3f vec_z = new vector3f();
                    vec_z.cross(vec_x, vec_y);
                    vec_z.normalize();

                    vec_x.cross(vec_z, vec_y);
                    vec_x.normalize();
                    vec_x.negate();

                    matrix3f series = new matrix3f(
                        vec_x.x, vec_x.y, vec_x.z,
                        vec_y.x, vec_y.y, vec_y.z,
                        vec_z.x, vec_z.y, vec_z.z
                    );
                    rotation.invert();