Vector Magnitude

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mikewill54

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Mar 7, 2016
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Hi
Hoping someone can help… I’m working through some vector problems and I can’t find my notes. I’m know the magnitude formula but I’m unsure how to combine terms in the following problem. Any help is appreciated.


The magnitude F (in newtons) of a force F and the magnitude G (in newtons) of a force G satisfy the vector equation

Fi+Gj−3/2Gi-18j=0

where i and j are the Cartesian unit vectors. What is the value of F (in newtons)?
Thanks
Mike
 
Hi Mike. I don't like seeing the same symbol used to simultaneously represent both a vector and a scalar, but maybe that's my problem.

The left-hand side of the equation shows a combination of horizontal and vertical vector components. Therefore, the zero on the right-hand side must represent the zero vector.

Thinking graphically, the zero-vector result means that, after moving all those vertical and horizontal displacements, we end up right back where we started (i.e., no net displacement).

Think about this. Starting at the Origin, we move F units in the i direction, and then we move -3G/2 units in the i direction, and we end up back at the Origin. In other words, the net horizontal displacement amount equals zero.

Can you think of an equation that you can write in terms of F and G to represent that?

Likewise, we can associate the two vertical displacement amounts and write an equation showing that they also combine to make zero.

Solve that system of two equations, to determine the scalars F and G.

?
 
Ok thanks
So I’m just combining like terms then substituting back in… I knew it was something simple
Thanks
Mike
 
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