Analytical methods

Definition

Analytical methods involve using mathematical techniques to solve problems related to vector addition and subtraction. These methods typically use trigonometry and algebra to find the magnitude and direction of resultant vectors.

5 Must Know Facts For Your Next Test

1. The components of a vector can be found using sine and cosine functions based on the angle from a reference axis.
2. To add or subtract vectors analytically, break each vector into its horizontal (x) and vertical (y) components.
3. The Pythagorean theorem is used to determine the magnitude of the resultant vector from its components.
4. The direction of the resultant vector can be determined by calculating the arctangent of the ratio between the y-component and x-component.
5. Analytical methods provide precise solutions which are often verified through graphical methods.

Review Questions

• How do you find the horizontal and vertical components of a vector given its magnitude and angle?
• What mathematical theorem is used to determine the magnitude of a resultant vector?
• How can you determine the direction angle of a resultant vector analytically?

Related terms

Vector: A quantity having both magnitude and direction, represented by an arrow.

Pythagorean Theorem: $$a^2 + b^2 = c^2$$, used to calculate the hypotenuse in a right triangle.

Arctangent: $\tan^{-1}(y/x)$, used to find an angle whose tangent is y/x.