# Addition of Perpendicular Vectors in two ways

• B
• Raabi Anony
In summary, the conversation discusses the concept of resolving a force vector into its components using trigonometry. The resulting components are found to be 70N each, which is verified using the Head-to-Tail method. However, there is a discrepancy when adding the components together, as they should equal the original force vector of 100N. The mistake is identified as not reconstituting the original force correctly. The conversation concludes with the acknowledgement of solving the issue and the individual plans to rephrase their question and return.
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
Fx = 100xCos(45) = 70N
Fy = 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?

Raabi Anony said:
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?

The hypotenuse of that right angled triangle is 100N.

Raabi Anony said:
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.

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

## What is the definition of perpendicular vectors?

Perpendicular vectors are two vectors that are at right angles to each other, meaning they form a 90-degree angle when plotted on a coordinate system.

## What are the two ways to add perpendicular vectors?

The two ways to add perpendicular vectors are by using the head-to-tail method or by using the Pythagorean theorem.

## Can you add more than two perpendicular vectors together?

Yes, you can add multiple perpendicular vectors together by using the same methods of head-to-tail or Pythagorean theorem.

## What is the result of adding perpendicular vectors in the same direction?

When adding perpendicular vectors in the same direction, the result is a vector with a magnitude equal to the sum of the individual vectors' magnitudes and a direction equal to the original direction.

## What is the result of adding perpendicular vectors in opposite directions?

When adding perpendicular vectors in opposite directions, the result is a vector with a magnitude equal to the difference of the individual vectors' magnitudes and a direction perpendicular to the original directions.

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