Unit 5 Formulas

Component form of a vector

magnitude of a vector <I,J>

square root of I^2 + J^2

direction of a vector <I,J>

tan-1 (J/I)
*May need to adjust quadrant

Dot product of two vectors

x * x + y * y

Angle between two vectors

𝑐𝑜𝑠𝜃 = 𝑢∙𝑣/‖𝑢‖‖𝑣‖

projection of u onto v

𝑝𝑟𝑜𝑗𝑣𝑢 = (𝑢∙𝑣/‖𝑣‖^2)v

Work formula (parallel)

work = force x distance
𝑊 =‖𝐹‖ ‖𝑃𝑄⃑⃑⃑⃑⃑ ‖

Work formula (not parallel)

𝑊 =𝑐𝑜𝑠𝜃 ‖𝐹‖ ‖𝑃𝑄⃑⃑⃑⃑⃑ ‖

Work formula when force and direction given as vectors

Dot product of force vector and direction vector

magnitude of a 3D vector

square root of (I^2 + J^2 + K^2)

Dot product of 3D vectors
𝒖=<𝒂,𝒃,𝒄> and 𝒗=<𝒅,𝒆,𝒇>

u∙𝑣 =𝑎𝑑+𝑏𝑒+𝑐𝑓