Addition of Perpendicular Vectors in two ways

[Raabi Anony]

I have a Force Vector = 100N, making an Angle = 45 degrees with x-axis.
When I find their Components trigonometrically, I get 70N each; as
F_x = 100xCos(45) = 70N
F_y = 100xSin(45) = 70N

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

Why is there discrepancy or where am I making a mistake?
Please help.

 

[sophiecentaur]

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

You are just adding them together arithmetically. Aren't they vectors in different directions (90 degrees)? What's the hypotenuse of that right angled triangle?

 

[Raabi Anony]

The hypotenuse of that right angled triangle is 100N.

 

[sophiecentaur]

The hypotenuse of that right angled triangle is 100N.

So the two components add together to produce the original force. The other two components will cancel because they are at 90 degrees to the original force. Your mistake was in not reconstituting the original force correctly.
Is there still a problem? I think we've solved your query.

 

[Raabi Anony]

Thanks for your time. Let me re-phrase my question and come back.