Vector Resultant and Pythagorean Theorem

6 Questions

The single vector that has the same effect as the individual vectors

To find the magnitude of the resultant vector when two vectors are added at right angles

It can be used to add vectors at any angle

Resolve each vector into its x- and y-components

Hypotenuse

Net vector or sum vector

Study Notes

The resultant of two or more vectors is the single vector that has the same effect as the individual vectors.
It is the vector sum of the individual vectors.
The resultant vector is also known as the net vector or the sum vector.

The Pythagorean Theorem is used to find the magnitude of the resultant vector when two vectors are added at right angles.
The theorem states: a² + b² = c², where a and b are the magnitudes of the two vectors, and c is the magnitude of the resultant vector.
The angle between the two vectors is 90 degrees.

The component method is a way to add vectors by breaking them down into their horizontal and vertical components.
The horizontal component is the x-component, and the vertical component is the y-component.
To add vectors using the component method:
1. Resolve each vector into its x- and y-components.
2. Add the x-components and y-components separately.
3. Use the resulting x- and y-components to find the magnitude and direction of the resultant vector.
The component method can be used to add vectors at any angle, not just at right angles.

The resultant of two or more vectors is the single vector that has the same effect as the individual vectors.
It is the vector sum of the individual vectors.
The resultant vector is also known as the net vector or the sum vector.

Used to find the magnitude of the resultant vector when two vectors are added at right angles.
The theorem states: a² + b² = c², where a and b are the magnitudes of the two vectors, and c is the magnitude of the resultant vector.
The angle between the two vectors is 90 degrees.

A way to add vectors by breaking them down into their horizontal and vertical components.
The horizontal component is the x-component, and the vertical component is the y-component.
The component method involves:
- Resolving each vector into its x- and y-components.
- Adding the x-components and y-components separately.
- Using the resulting x- and y-components to find the magnitude and direction of the resultant vector.
The component method can be used to add vectors at any angle, not just at right angles.