MA113 HELL

v\|v|

v\|v|

unit vector in direction of v (T)

θ=cos⁻¹(u.v\|u||v|)

Finding angle using dot product

u.v = 0

u and v are orthogonal

uxv = 0

u and v are parallel

rxF

Torque Formula

d = |PSxv|\|v|

Distance from a line to a point

|v| (physics)

speed

(v₀ cosα)ti + ((v₀sinα)t - .5gt²)j

Ideal projectile motion equation

(v₀sinα)²\2g

Maximum height

(2v₀sinα)\g

time taken

(v₀²sin2α)\g

range

∫√(x’²+y’²+z’²)dt

Arc length formula

κ = |dT\dt|\|v|

curvature formula

N = (dT\dt)\|dT\dt|

normal vector formula

|v|\dt

TNB “At”

κ|v|²

TND “An”

δf\δxi + δf\δyj

gradient formula

∨f.u

Directional Derivative at a point in the direction of u

fxx<0 and fxxfyy-fxy²>0

local maximum

fxx>0 and fxxfyy-fxy²>0

local min

fxxfyy-fxy²<0

saddle point

1/area of R∫∫dA

Average value of f over R

∫∫r dr dθ

polar form

∫∫∫ x δ dV

Myz

∫∫∫ y δ dV

Mxz

∫∫∫ z δ dV

Mxy

∫∫∫δ dV

Mass