Vectors Intro Formulas

Geometric Vector

represented by a line w/ an arrow on one end

Algebraic Vector

a set of coordinates (a, b) representing the horizontal and vertical components of the vector respectively

Position Vector

geometric vector from origin to any point P

Displacement Vector

geometric vector from point A to point B

Equivalent/Equal Vector

2 vectors that have the same magnitude AND direction

Opposite Vector

2 vectors that have the same magnitude but point in OPPOSITE directions

Parallel Vector

2 vectors that have either the same or opposite direction, DO NOT HAVE TO HAVE SAME MAGNITUDE

formula w/ x for direction angles and scalar components of vector

x = | ⃗v| cos α

formula w/ y for direction angles and scalar components of vector

y = | ⃗v| cos β

formula w/ z for direction angles and scalar components of vector

z = | ⃗v| cos γ

algebraic displacement vector formula

 ⃗AB = (x₂ -x₁)î + (y₂ - y₁)ĵ - (for R²)

OR

 ⃗AB = (x₂ -x₁)î + (y₂ - y₁)ĵ + (z₂ - z₁)k̂ - (for R³)

For any vector v⃑ , a unit vector parallel to v⃑ is given by:

v̂ = v⃑ / |v⃑ |