# Addition of Perpendicular Vectors in two ways

Vectors in geometry

### Addition of Perpendicular Vectors in two ways

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?
Guest

### Re: Addition of Perpendicular Vectors in two ways

Hi!

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

I hope I have helped!

Baltuilhe

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### Re: Addition of Perpendicular Vectors in two ways

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!

HallsofIvy

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