Vinkel ml. vektorer (bevis) | Desmos

- 2 ⋅ | a→ | ⋅ | b→ | ⋅ cos v ⇔

26

- 2 ⋅ a→ ⋅ b→ =

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- 2 ⋅ | a→ | ⋅ | b→ | ⋅ cos v ⇔

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a→ ⋅ b→ =

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| a→ | ⋅ | b→ | ⋅ cos v ⇔

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cos v =

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( a→ ⋅ b→ ) / ( | a→ | ⋅ | b→ | )

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Bevis 2

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Video 12: https://goo.gl/mswkKE

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a→ = ( | a→ | ; 0 )

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b→ =

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( | b→ | ⋅ cos v ; | b→ | ⋅ sin v )

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a→ ⋅ b→ =

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| a→ | ⋅ | b→ | ⋅ cos v ⇔

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cos v =

40

( a→ ⋅ b→ ) / ( | a→ | ⋅ | b→ | )

41

Punkter

42

Pilespidser

49

Expression 50: left parenthesis, StartFraction, "b" Subscript, 1 , Baseline Over 1.6 , EndFraction minus StartFraction, cos 0.1 Over 8 , EndFraction "t" , StartFraction, "b" Subscript, 2 , Baseline Over 1.6 , EndFraction minus StartFraction, sin 0.1 Over 8 , EndFraction "t" , right parenthesis Has graph.

0

domain t Minimum:

less than or equal to "t" less than or equal to

1

domain t Maximum:

50

Expression 51: left parenthesis, StartFraction, "b" Subscript, 1 , Baseline Over 1.6 , EndFraction minus StartFraction, cos .8 5 Over 8 , EndFraction "t" , StartFraction, "b" Subscript, 2 , Baseline Over 1.6 , EndFraction minus StartFraction, sin .8 5 Over 8 , EndFraction "t" , right parenthesis Has graph.

0

domain t Minimum:

less than or equal to "t" less than or equal to

1

domain t Maximum:

51

Expression 52: left parenthesis, "b" Subscript, 1 , Baseline plus StartFraction, "a" Subscript, 1 , Baseline minus "b" Subscript, 1 , Baseline Over 2.5 , EndFraction plus StartFraction, cos negative 0.4 Over 8 , EndFraction "t" , StartFraction, "b" Subscript, 2 , Baseline Over 1.6 7 , EndFraction plus StartFraction, sin negative 0.4 Over 8 , EndFraction "t" , right parenthesis Has graph.

0

domain t Minimum:

less than or equal to "t" less than or equal to

1

domain t Maximum:

52

Expression 53: left parenthesis, "b" Subscript, 1 , Baseline plus StartFraction, "a" Subscript, 1 , Baseline minus "b" Subscript, 1 , Baseline Over 2.5 , EndFraction plus StartFraction, cos negative 1.2 Over 8 , EndFraction "t" , StartFraction, "b" Subscript, 2 , Baseline Over 1.6 7 , EndFraction plus StartFraction, sin negative 1.2 Over 8 , EndFraction "t" , right parenthesis Has graph.

0

domain t Minimum:

less than or equal to "t" less than or equal to

1

domain t Maximum:

53

Expression 54: left parenthesis, 1.5 plus StartFraction, cos negative 0.4 Over 8 , EndFraction "t" , 0 plus StartFraction, sin negative 0.4 Over 8 , EndFraction "t" , right parenthesis Has graph.

0

domain t Minimum:

less than or equal to "t" less than or equal to

1

domain t Maximum:

54

Expression 55: left parenthesis, 1.5 plus StartFraction, cos .3 5 Over 8 , EndFraction "t" , 0 plus StartFraction, sin .3 5 Over 8 , EndFraction "t" , right parenthesis Has graph.

0

domain t Minimum:

less than or equal to "t" less than or equal to

1

domain t Maximum:

55

Vinkelbue

56

Expression 57: left parenthesis, 0.7 5cos "t" , 0.7 5sin "t" left brace, 0 less than or equal to "t" less than or equal to cos to the negative 1st power "C" Subscript, "V" , Baseline , right brace , right parenthesis Has graph.

domain t Minimum: 0

less than or equal to "t" less than or equal to

domain t Maximum: tau

57

25.56 ° left parenthesis, 1 half , 0.1 0 3 , right parenthesis equals left parenthesis, 0.5 , 0.1 0 3 , right parenthesis

Label:

equals

left parenthesis, 0.5 , 0.1 0 3 , right parenthesis

58

59

powered by

powered by

left parenthesis, "a" Subscript, 1 , Baseline ; "a" Subscript, 2 , Baseline , right parenthesis

left parenthesis, "b" Subscript, 1 , Baseline ; "b" Subscript, 2 , Baseline , right parenthesis

negative "a" to

"b" to

"b" to negative "a" to

25.56 °

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