Addition of Perpendicular Vectors in two ways

Vectors in geometry

Addition of Perpendicular Vectors in two ways

Postby Guest » Sun Aug 12, 2018 9:58 am

I have a Force Vector = 100N, making an Angle = 45 degrees.
When I find their Components trigonometrically, I get 70N each; as
Fx = 100xCos(45) = 70N
Fy = 100xSin(45) = 70N

Verifying the result, by Head-to-Tail method, I get 70N + 70N = 140N.

Where am making a mistake?
Please help.
Guest
 

Re: Addition of Perpendicular Vectors in two ways

Postby Baltuilhe » Sat Dec 15, 2018 1:48 pm

Hi!

You have to consider that both vector (70) are perpendicular between themselves. So, using a right triangle:
[tex]S^2=70^2+70^2=4900*2=9800\\S=\sqrt{9800}\approx 100[/tex]

I hope I have helped! :)

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Re: Addition of Perpendicular Vectors in two ways

Postby HallsofIvy » Thu Mar 14, 2019 8:43 pm

A vector of length "a" added to a vector of length "b" would give a vector of length "a+ b" only if the vectors in the same direction!

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