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Questions and Answers
What is the purpose of the parallelogram method in vector calculations?
To add or subtract vectors.
How do you find the horizontal and vertical components of a vector?
Resolve the vector into its horizontal and vertical components using trigonometry.
What is the method used to find the resultant of more than 2 vectors?
Draw a vector polygon.
What is the procedure called when a vector is broken down into its horizontal and vertical components?
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What is the condition for the resultant of vectors to be zero?
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In resolving a vector, what are the two components that a vector can be broken down into?
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What trigonometric function is used to find the horizontal component of a vector?
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What is the advantage of resolving a vector into two perpendicular components?
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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?
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What is the significance of equilibrium in problems involving vectors?
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Study Notes
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).
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Description
Quiz about vector addition, trigonometry and calculating resultant vectors using trigonometric methods. Covers finding components of vectors and calculating their resultant.
