Vectors: Understanding and Calculating Resultant of 3 Vectors with Magnitude 10m

[shibu]

Hi,
I am new to physics, and have been trying to understand some basic concepts using University Physics by Harris Benson. I had a query on vectors. Would appreciate all the help.
So here is the problem.

If there are three vectors with equal magnitudes of 10m, how should the vectors be aligned to get a resultant of 20m? And how can it be demonstrated using a diagram?

 

[Dale]

Hi Shibu, welcome to PF!

There are an infinite number of arrangements that satisfy this. You have three degrees of freedom (direction of each of the three vectors) and only one constraint (length of the sum).

 

[niklaus]

One possibility that is easy for me to visualize would be to arrange them in a trapezoid, with the resultant as the longest edge. But as DaleSpam said, that is just one out of an infinite number of possibilities, even if you restrict yourself to two timensions.

 

[shibu]

Hi DaleSpam and Niklaus,

Thanks for the replies. The thing is i haven't graduated to three-dimension vectors as yet. Still trying to master two-dimensions!

Now, if the three vectors were on a plane, I know how to get a resultant that measures 0 m (the resultant of the first two vectors has to be the negative of the third), 10 m (two vectors are parallel, and one is anti-parallel), and 30 m (all the three vectors are parallel). But how to I get a resultant that measures 20 m? How do I deconstruct the problem with the given data, which is that the three vectors have equal magnitudes of 10m? Can you help me with an example?

Regards

 

[niklaus]

It seems like you are stuck in 1D and need to move on to 2D... In a plane, vectors can point in any direction and be at any angle relative to each other, not just parallel or antiparallel. I think once you see that it should be obvious.To come back to the example of the trapezoid mentioned before: (this would be easier if I could draw it but I'll try to describe it to you) draw the resultant first from left to right. Then at an angle of 60 degrees draw the first vector (originating from the same point as the resultant). Then at the end point of that vector draw the second one parallel to the resultant, and the third one connecting the end point of that one with the end point of the resultant.

 

[shibu]

Lovely, that IS quite helpful. Thanks Niklaus.