oef vecteurs --- Introduction ---

This modulus contains at this moment 10 simple exercises on vectors and their applications in physics on the following subjects:

Chiffres significatifs


( )

Relation entre trois vecteurs


xrange -200,200 yrange -200,200 arrow -50+,0+,50+,0+,10,red text red,,-10,large, arrow 0+,-50+,0+,50+,10,blue text blue,+10,,large, arrow -50+,-50+,50+,50+,10,green text green,+10,,large, xrange -200,200 yrange -200,200 arrow -50+,-50+,50+,50+,10,red text red,,-10,large, arrow 50+,-50+,-50+,50+,10,blue text blue,+10,+20,large, arrow ,-100+,,100+,10,green text green,+10,,large, xrange -200,200 yrange -200,200 arrow -50+,50+,50+,-50+,10,red text red,-30,,large, arrow -50+,-50+,50+,50+,10,blue text blue,+10,,large, arrow -100+,,100+,,10,green text green,,-10,large,

Mobile en rotation

Un mobile décrit un cercle de rayon R= m (représenté en jaune sur la figure), à vitesse uniforme V= m/s. A un instant donné, la position du mobile, , est représentée par le vecteur bleu , et sa vitesse, , par le vecteur rouge.
  • Calculer les coordonnées cartésiennes de et Ry(m) =
  • Calculer les coordonnées cartésiennes de et Vy(m) =
(On donnera les réponses avec 3 chiffres significatifs). An object is moving with a circular trajectory of radius R= m (represented in yellow in the figure) with a uniform velocity V= m/s. At a given instant, the position of the object, , is represented by the blue vector , and its velocity, , by the red vector.
  • Calculate the Cartesian coordinates of and Ry(m) =
  • Calculate the Cartesian coordinates of and Vy(m) =
(Please write the answers using 3 significant figures).
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Angle entre deux vecteurs (<90°)

Deux vecteurs unitaires ,
  • (représenté en )
  • et (représenté en ),
ont pour coordonnées cartésiennes les valeurs suivantes:
  • ax = et ay =
  • bx = et by =
A l'aide du produit scalaire, déterminer l'angle entre ces deux vecteurs. On donnera la réponse arrondie au degré le plus proche. Two unit vectors,
  • (represented by )
  • et (represented by ),
are defined by the following values of their Cartesian coordinates:
  • ax = and ay =
  • bx = and by =
Use the scalar product to determine the angle between these two vectors. Please give the answer rounded to the nearest degree.
= deg
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Angle entre deux vecteurs (>90°)

Deux vecteurs unitaires ,
  • (représenté en )
  • et (représenté en ),
ont pour coordonnées cartésiennes les valeurs suivantes:
  • ax = et ay =
  • bx = et by =
A l'aide du produit scalaire, déterminer l'angle entre ces deux vecteurs. On donnera la réponse arrondie au degré le plus proche. Two unit vectors ,
  • (represented by )
  • et (represented by ),
are defined by the following values of their Cartesian coordinates:
  • ax = and ay =
  • bx = and by =
Use the scalar product to determine the angle between these two vectors. Please round the answer to the nearest degree.
= deg
xrange -100,100 yrange -100,100 arrow -100,0,100,0,10,black arrow 0,-100,0,100,10,black text black,92,-10,large,x text black,10,95,large,y text black,-10,-10,large,0 arrow 0,0,80*,80*,14, arrow 0,0,80*,80*,14, arc 0,0,40,40,,,red text red,50*cos((+/2)/180*3.1416),50*sin((+/2)/180*3.1416),large,?

Projection d'un vecteur

Deux vecteurs , (représenté en bleu ) et (représenté en vert ) , ont pour coordonnées catésiennes les valeurs suivantes:
Ax = cm et Ay = cm
Bx = cm et By = cm
  • Quelle est la norme du vecteur ?
    A= cm
  • A l'aide du produit scalaire, déterminer la longueur du segment OH, projection de sur la direction de .
    OH = cm
On donnera les réponses avec 3 chiffres significatifs. Two vectors , (represented in blue ) and (represented in green ) , are define by the following value of their Cartesian units:
Ax = cm and Ay = cm
Bx = cm and By = cm
  • What is the norm of the vector?
    A= cm
  • Use the scalar product to determine the length of th OH segment, projection of on the direction of .
    OH = cm
Please give the answers with 3 significant figures.
xrange -100,100 yrange -100,100 arrow -100,0,100,0,10,black arrow 0,-100,0,100,10,black text black,92,-10,large,x text black,10,95,large,y text black,5,-6,large,0 arrow 0,0,,,14,blue arrow 0,0,,,14,green dline ,,,,red text red,,,large,H

Combinaison de vecteurs

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p=
q=

Travail d'une force


     
A(,,)
  • B(,,)


  • (J)=

    Bloc sur un plan incliné

    • m= kg N.
    • .
    L=

    WF (kJ) =
    WP (kJ) =
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    Système de coordonnées direct /indirect




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    The most recent version


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    Description: exercices de bases (pour physiciens) sur les vecteurs. interactive exercises, online calculators and plotters, mathematical recreation and games

    Keywords: interactive mathematics, interactive math, server side interactivity, physics, vecteur, addition, composition, coordonnees, produit scalaire, norme, physique, mécanique