The basics Flashcards by Tom Truax Weston

Q

V!+W!

A

W!+V!

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Q

a(bW!)

A

(ab)W!

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Q

(V!+W!)+U!

A

V!+(W!+U!)

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Q

(a+b)V!

A

aV!+bV!

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Q

1V!

A

V!

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Q

0V!

A

0!

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Q

V!+0!

A

V!

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Q

W!+(-1)U!

A

W!-U!

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Q

V! * W!

A

W! * V!

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Q

(aV!)W!=V!(aW!)

A

a(V!*W!)

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Q

(V!+W!)U!=V!U! + W!*U!

A

IIV!II^2=V!*V!

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Q

If V! and W! are parallel

A

V! x W! = 0

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Q

U! x (V! + W!)=

A

U! x V! + U! x W!

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Q

V! x W!

A

-W! x V!

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Q

(aV!) x (W!) = V! x (aW!)

A

a(V! x W!)

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Q

area of a parallelogram

A

IIV! x W!II

Q

area of a triangle

A

1/2 IIV! * W!II

Q

arithmetic equation dot product

A

V!xW!x+V!yW!y+V!zW!z

Q

geometric equation dot product

A

IIV!II IIW!II cos(theta)

Q

normal vector

A

is perpendicular to plane

Q

normal vector plane equation

A

PoP! * n! = a(x-xo)+b(y-yo)+c(z-z0)

Q

unit vector

A

V!/IIV!II

Q

unit vector over a certain distance

A

dV!/IIV!II

Q

geometric equation for cross product magnitude

A

IIV! x W!II = IIW!II IIV!II sin(theta)

Q

geometric equation for cross product

A

V! x W! = IIV!II IIW!II sin(theta) n!

Q

matrix for agebraic cross product

A

V! x W! = (V2W3 - V3W2)i! - (V1W3-V3W1)j! + (V1W2-V2W1)K!

Q

A