MA113 HELL

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27 Terms

1
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v\|v|

unit vector in direction of v (T)

2
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θ=cos⁻¹(u.v\|u||v|)

Finding angle using dot product

3
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u.v = 0

u and v are orthogonal

4
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uxv = 0

u and v are parallel

5
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rxF

Torque Formula

6
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d = |PSxv|\|v|

Distance from a line to a point

7
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|v| (physics)

speed

8
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(v₀ cosα)ti + ((v₀sinα)t - .5gt²)j

Ideal projectile motion equation

9
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(v₀sinα)²\2g

Maximum height

10
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(2v₀sinα)\g

time taken

11
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(v₀²sin2α)\g

range

12
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∫√(x’²+y’²+z’²)dt

Arc length formula

13
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κ = |dT\dt|\|v|

curvature formula

14
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N = (dT\dt)\|dT\dt|

normal vector formula

15
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|v|\dt

TNB “At”

16
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κ|v

TND “An”

17
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δf\δxi + δf\δyj

gradient formula

18
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∨f.u

Directional Derivative at a point in the direction of u

19
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fxx<0 and fxxfyy-fxy²>0

local maximum

20
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fxx>0 and fxxfyy-fxy²>0

local min

21
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fxxfyy-fxy²<0

saddle point

22
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1/area of R∫∫dA

Average value of f over R

23
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∫∫r dr dθ

polar form

24
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∫∫∫ x δ dV

Myz

25
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∫∫∫ y δ dV

Mxz

26
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∫∫∫ z δ dV

Mxy

27
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∫∫∫δ dV

Mass