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A vector that is 7.1 units long and a vector that is 5.0 units long are added. Their sum is a vector 7.6 units long. (a) Show graphically at least one way that the vectors can be added. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Using your sketch in Part (a), determine the angle between the original two vectors. °

Respuesta :

Answer:

[tex]\theta=119.8138^{\circ}[/tex]

Explanation:

Given:

  • magnitude of first vector, [tex]A=7.1\ units[/tex]
  • magnitude of second vector, [tex]B=5.0\ units[/tex]
  • resultant of magnitude of the two vectors, [tex]R=7.6\ units[/tex]

a)

From the vector addition rule we know:

[tex]R^2={A^2+B^2+2A.B\cos\theta}[/tex]

where

[tex]\theta=[/tex] angle between the two vectors with their tail at common point.

b)

Putting respective values:

[tex]7.6^2=7.1^2+5^2+7.1\times 5\times \cos \theta[/tex]

[tex]\theta=119.8138^{\circ}[/tex]

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