Vector Addition and Trigonometry

What is the purpose of the parallelogram method in vector calculations?

How do you find the horizontal and vertical components of a vector?

What is the method used to find the resultant of more than 2 vectors?

What is the procedure called when a vector is broken down into its horizontal and vertical components?

What is the condition for the resultant of vectors to be zero?

In resolving a vector, what are the two components that a vector can be broken down into?

What trigonometric function is used to find the horizontal component of a vector?

What is the advantage of resolving a vector into two perpendicular components?

In a problem involving bill traveling 10km North-east and then 12km due East, how would you calculate Bill's resultant displacement in components East and North?

What is the significance of equilibrium in problems involving vectors?

Vectors and Forces

The sine rule can be used to find an angle or a side, with sines on top or bottom depending on the problem.
The parallelogram method can be used to add or subtract vectors.
To find the magnitude of the resultant, use the vector triangle or parallelogram method.

Resolving Vectors

Resolving a vector involves finding its components in two perpendicular directions.
Use a right-angled triangle with the vector as the hypotenuse and the desired directions as the other two sides.
Use trigonometry to find the size of the components.

Components of Vectors

Components can be found using the sine and cosine rules.
The component parallel to a direction is given by the cosine of the angle between the vector and the direction.
The component perpendicular to a direction is given by the sine of the angle between the vector and the direction.

Resultant of Multiple Vectors

To find the resultant of more than two vectors, draw a vector polygon.
The resultant is the vector that closes the polygon.
If the polygon closes, the resultant is zero.

Exam Hints

In practical problems, resolve vectors into horizontal and vertical components.
If an inclined plane is involved, resolve vectors along and perpendicular to the plane.
Use trigonometry to find components and resultants.

Typical Exam Questions

Draw a vector diagram showing a route or displacement.
Calculate the resultant displacement in components (e.g. East and North).

Quiz about vector addition, trigonometry and calculating resultant vectors using trigonometric methods. Covers finding components of vectors and calculating their resultant.