Finding Magnitude and Direction of Vector Addition and Subtraction

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.
  • #1
luckylayla
2
0
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?
 
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  • #2
Try drawing it out firstly and what does A+B mean in vector notation? (How do you 'add' two vectors?)
 

FAQ: Finding Magnitude and Direction of Vector Addition and Subtraction

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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