( ( ( ( ( ( A vector ) ( ( defines ( ( magnitude and ) direction ) ) ( by ( ( ( giving ( a point ) ) and ) ( saying ( ( its magnitude ) ( ( ( is ( its distance ) ) ( from head ) ) ( to tail ) ) ) ) ) ) ) ) , ) and ) ( ( its direction ) ( is ( ( its displacement ) ( in ( ( the ( reverse-clockwise direction ) ) ( from ( the ( positive ( x axis ) ) ) ) ) ) ) ) ) ) . )
(ROOT (S (S (NP (DT A) (NN vector)) (VP (VBZ defines) (NP (NN magnitude) (CC and) (NN direction)) (PP (IN by) (S (VP (VP (VBG giving) (NP (DT a) (NN point))) (CC and) (VP (VBG saying) (SBAR (S (NP (PRP$ its) (NN magnitude)) (VP (VBZ is) (NP (PRP$ its) (NN distance)) (PP (IN from) (NP (NN head))) (PP (TO to) (NP (NN tail)))))))))))) (, ,) (CC and) (S (NP (PRP$ its) (NN direction)) (VP (VBZ is) (NP (NP (PRP$ its) (NN displacement)) (PP (IN in) (NP (NP (DT the) (JJ reverse-clockwise) (NN direction)) (PP (IN from) (NP (DT the) (JJ positive) (CD x) (NNS axis)))))))) (. .)))
A vector defines magnitude and direction by giving a point and saying its magnitude is its distance from head to tail, and its direction is its displacement in the reverse-clockwise direction from the positive x axis.
(ROOT (S (NP (NNP Distance)) (VP (VBZ is) (VP (VBN defined) (PP (IN as) (NP (NP (DT the) (NN magnitude) (CC or) (NN size)) (PP (IN of) (NP (NP (NN displacement)) (PP (IN between) (NP (CD two) (NNS positions))))))))) (. .)))