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Questions and Answers
What are the x and y components of vector a?
What are the x and y components of vector a?
- a_x = a tan(theta), a_y = a cot(theta)
- a_x = a cos(theta), a_y = a sin(theta) (correct)
- a_x = a sin(theta), a_y = a cos(theta)
- a_x = a cot(theta), a_y = a tan(theta)
What are the x and y components of the vector sum?
What are the x and y components of the vector sum?
- Sum_x = (a - b) sin(theta), Sum_y = (a + b) cos(theta)
- Sum_x = (a - b) cos(theta), Sum_y = (a - b) sin(theta)
- Sum_x = (a + b) cos(theta), Sum_y = (a + b) sin(theta) (correct)
- Sum_x = (a + b) sin(theta), Sum_y = (a - b) cos(theta)
What is the angle axis 'a' makes with the positive direction of the x-axis?
What is the angle axis 'a' makes with the positive direction of the x-axis?
- cos^-1(a_y/a_x)
- tan^-1(a_y/a_x) (correct)
- sin^-1(a_y/a_x)
- (a_y/a_x)
What is the magnitude of vector a?
What is the magnitude of vector a?
What is the magnitude of vector b?
What is the magnitude of vector b?
What are the x and y components of the vector sum?
What are the x and y components of the vector sum?
What is the angle 'θ' that vector a makes with the positive direction of the x-axis?
What is the angle 'θ' that vector a makes with the positive direction of the x-axis?
What are the unit vectors pointing in the positive directions of x, y, and z axes represented as?
What are the unit vectors pointing in the positive directions of x, y, and z axes represented as?
Flashcards
Vector 'a' components?
Vector 'a' components?
a_x = a cos(θ), a_y = a sin(θ)
Sum vector components?
Sum vector components?
Sum_x = (a + b) cos(θ), Sum_y = (a + b) sin(θ)
Angle of vector 'a'?
Angle of vector 'a'?
tan⁻¹(a_y / a_x)
Magnitude of vector 'a'?
Magnitude of vector 'a'?
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Vector sum components?
Vector sum components?
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Angle θ of vector 'a'?
Angle θ of vector 'a'?
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Study Notes
Vector Components
- Vectors can be broken down into x and y components, allowing for easier calculations in two-dimensional space.
- The x-component represents the horizontal influence of the vector, while the y-component signifies the vertical influence.
Vector Sum
- The vector sum combines the x and y components of two or more vectors, yielding new x and y components for the resulting vector.
- The resulting vector is crucial in determining the overall direction and magnitude of multiple vector influences.
Angles with X-axis
- The angle that vector 'a' makes with the positive x-axis can be calculated using trigonometric functions (often utilizing the tangent function).
- This angle provides insight into the direction of the vector in relation to the horizontal axis.
Magnitudes of Vectors
- The magnitude of a vector indicates its length, typically calculated using the Pythagorean theorem applied to its components (√(x² + y²)).
- Each vector has a specific magnitude that defines its strength or intensity in a physical context.
Unit Vectors
- Unit vectors in three-dimensional space are represented as follows:
- î for the x-axis
- ĵ for the y-axis
- k̂ for the z-axis
- These unit vectors serve as the foundation for expressing any vector's direction in a standardized format.
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