# Adding Vectors: Find Resultant Magnitude of P + S

• leetnerdgirl
In summary: PllllSIn summary, to find the magnitude of the resultant of adding vectors P and S, you can use the Pythagorean Theorem by setting up a triangle on a coordinate system and solving for the hypotenuse, which is the magnitude of the resultant vector. Alternatively, you can use the square root of the sum of the squares of the two vectors. By drawing out the vectors on a coordinate system, you can see that the magnitude is the hypotenuse of the triangle, which can be solved using the Pythagorean Theorem (P^2 + S^2 = C^2). In this case, the magnitude is 5.39 units.
leetnerdgirl
Okay I've been given a question about adding and subtracting vectors, and my physics teacher didn't even explain anything at all.

Q1) What is the magnitude of the resultant of the addition of the vector P + S? Where P is 2 units north and S is 5 units east.

I think I'd have to use Pythagoras' Theorem but seriously, I have no idea how to do this so if someone could PLEASE explain in detail and go through all the steps that would be awesome.
Thanks.

Draw it out on a coordinate system, and know that vectors P,S add head-to-tail. With this you can set up a triangle, and solve for the resultant vector, R. The constant of that resultant vector is the magnitude of that vector.

Ultimately, you could have just used the squareroot of the sum of the squares deal to get it from the start, but draw it out so you understand the concept of vector addition.

Your magnitude will be the Sqrt. of (2^2 + 5^2) which equals 5.39 units. It's basically the pythagorean thm. If you draw the vectors out you will have a leg 2 units long pointing straight up (north) and then you will have another leg 5 units long pointing in the right direction (east). Since you have the values of the two "legs" you can look at the magnitude of the vector as the hypoteneuse of the triangle. Therefore in your case P^2 + S^2 = C^2, solve for C and there is your magnitude.

Edit: It will look like this crappy rendering below (each dash = 1 unit), just connect the two ends with a hypoteneuse and solve for the length of it.

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## 1. What is the formula for finding the resultant magnitude of P + S?

The formula for finding the resultant magnitude of P + S is: |P + S| = √(Px² + Py² + Pz² + Sx² + Sy² + Sz²), where Px, Py, and Pz are the x, y, and z components of vector P and Sx, Sy, and Sz are the x, y, and z components of vector S.

## 2. How do I add vectors P and S?

To add vectors P and S, you must first find the x, y, and z components of each vector. Then, add the corresponding components of P and S to get the resultant vector. The resultant vector will have x, y, and z components that represent the combined effect of P and S.

## 3. Can the resultant magnitude of P + S be negative?

No, the resultant magnitude of P + S cannot be negative. Magnitude is a measure of the size or length of a vector, and it is always a positive value. If the resultant vector has a negative component, it means that the vector is pointing in the opposite direction of the positive axis.

## 4. What is the difference between magnitude and direction of a vector?

Magnitude refers to the size or length of a vector, while direction refers to the orientation or angle of the vector. Both magnitude and direction are necessary to fully describe a vector.

## 5. What if vector P and S are not in the same plane?

If vector P and S are not in the same plane, you will need to use the Pythagorean theorem to find the resultant magnitude. This is because the formula for finding the resultant magnitude assumes that the vectors are in the same plane. You will also need to use trigonometry to find the angle between the resultant vector and the x-axis.

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