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Hint

1

**v**\|**v**|

unit vector in direction of **v **(**T**)

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2

θ=cos⁻¹(**u.v**\|**u**||**v**|)

Finding angle using dot product

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3

**u.v** = 0

**u **and **v** are orthogonal

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4

**u**x**v** = 0

**u** and **v** are parallel

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5

**r**x**F**

Torque Formula

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6

d = |**PS**x**v**|\|**v**|

Distance from a line to a point

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7

|**v**| (physics)

speed

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8

(v₀ cosα)t**i** + ((v₀sinα)t - .5gt²)**j**

Ideal projectile motion equation

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9

(v₀sinα)²\2g

Maximum height

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10

(2v₀sinα)\g

time taken

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11

(v₀²sin2α)\g

range

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12

∫√(x’²+y’²+z’²)dt

Arc length formula

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13

κ = |d**T**\dt|\|**v**|

curvature formula

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14

N = (d**T**\dt)\|d**T**\dt|

normal vector formula

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15

|**v**|\dt

TNB “At”

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16

κ|**v**|²

TND “An”

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17

δf\δx**i** + δf\δy**j**

gradient formula

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18

∨f.**u**

Directional Derivative at a point in the direction of **u**

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19

fxx<0 and fxxfyy-fxy²>0

local maximum

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20

fxx>0 and fxxfyy-fxy²>0

local min

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21

fxxfyy-fxy²<0

saddle point

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22

1/area of R∫∫dA

Average value of f over R

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23

∫∫r dr dθ

polar form

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24

∫∫∫ x δ dV

Myz

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25

∫∫∫ y δ dV

Mxz

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26

∫∫∫ z δ dV

Mxy

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27

∫∫∫δ dV

Mass

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