# Finding Magnitude and Direction of Vector Addition and Subtraction

• luckylayla
In summary, vector addition and subtraction are mathematical operations used to find the magnitude and direction of a resultant vector when combining two or more vectors. The magnitude of a vector can be found using the Pythagorean theorem, and its direction is the angle it makes with the positive x-axis. To add or subtract vectors, they must first be resolved into their x and y components, and then the components can be added or subtracted separately to find the resultant vector's magnitude and direction.
luckylayla
vector A has a magnitude of 81 units and points due west, while vector B has the same magnitude and points due south. Find the magnitude and direction of (a) A + B and (b) A - B . Specify the directions relative to due west.

(a) Magnitude and direction of A + B = and o
(b) Magnitude and direction of A - B = and o
Hi folks any idea?

Try drawing it out firstly and what does A+B mean in vector notation? (How do you 'add' two vectors?)

## 1. What is vector addition and subtraction?

Vector addition and subtraction are mathematical operations used to find the magnitude and direction of a resultant vector when two or more vectors are combined. Vectors are quantities that have both magnitude (size) and direction.

## 2. How do you find the magnitude of a vector?

The magnitude of a vector is found by using the Pythagorean theorem, which states that the square of the hypotenuse (longest side) of a right triangle is equal to the sum of the squares of the other two sides. So, to find the magnitude of a vector, you can square the individual components of the vector, add them together, and then take the square root of the sum.

## 3. What is the direction of a vector?

The direction of a vector is the angle it makes with the positive x-axis, measured counterclockwise. It is usually expressed in either degrees or radians.

## 4. How do you add vectors?

To add vectors, you first need to resolve them into their x and y components. Then, you can add the components of each vector separately to find the x and y components of the resultant vector. Finally, use the Pythagorean theorem to find the magnitude of the resultant vector and trigonometry to find the direction.

## 5. Can vectors be subtracted?

Yes, vectors can be subtracted in the same way that they are added. You just need to remember that when subtracting a vector, you are essentially adding its negative. So, you would need to flip the direction of the vector before resolving it into components and following the same steps as vector addition.

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