Can vector arrows be “extended”?

Hello, I'm currently studying forces as vectors in physics. I came across the following problem:

I calculated this using cosine as follows.

  1. F1= cos(30)*400=346.4N
  2. F2= cos(60)*400=200N

I've basically enlarged the vector arrows to create a triangle with right angles. Is this allowed? Thanks for looking 🙂

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Hamburger02
3 months ago

Only the length of the green vector with F=400 N is given. It must not be extended… except for a new scale. The two red vectors are not given from their amount, but only from their direction. The length is to be determined, which will then also change its length.

Clemens1973
3 months ago

For your account: the solutions for F1 and F2 are not correct yet. It must apply

2 Equations for the two unknowns F1 and F2. The second equation must apply because otherwise a force component perpendicular to the force F acts.

PS: I now understand what you mean by “extending” the vector arrows. Projecting F to F1 and F2 is, however, not sensible; the F1 and F2 thus obtained do not add vectorially to the force F. F1 and F2 have to form a parallelogram whose diagonal is equal to F–the angles are generally not perpendicular.

Kelec
3 months ago

On the one hand it depends on what the drawing is supposed to represent and on the other what you mean to extend.

Of course, you may use auxiliary lines in each drawing, but if the drawing is to depict the vectors themselves and not only sketch the vectors, of course you must not extend the vectors.

Scheibenpiekser
3 months ago

Take the force F as a hypotenuse, you catch F1. So much is right. Since both angles together result in 90°, you can move F2 as a counter catheter of Angle Alpha. Then apply the phrase of Pythagoras.

Scheibenpiekser
3 months ago

Your calculations are correct. And all vectors yield a rectangular triangle. What’s the problem now?

Prism97
3 months ago

I don’t quite understand what vector arrows mean, but the calculation is correct.

priesterlein
3 months ago

Vectors usually express a numerical value by their length and are Length and direction defined: You can’t just extend it like that.