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Questions and Answers
What does a vector quantity possess?
What does a vector quantity possess?
How are vectors represented in this book?
How are vectors represented in this book?
What does |v| represent for a vector v?
What does |v| represent for a vector v?
How are vectors often represented when written by hand?
How are vectors often represented when written by hand?
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When are two vectors A and B considered equal?
When are two vectors A and B considered equal?
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What is represented by the vector PP′?
What is represented by the vector PP′?
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What are vectors with fixed locations called?
What are vectors with fixed locations called?
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When multiplying a vector A by a positive number λ, what changes?
When multiplying a vector A by a positive number λ, what changes?
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What happens when a vector is displaced parallel to itself?
What happens when a vector is displaced parallel to itself?
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What are vectors with an important location or line of application called?
What are vectors with an important location or line of application called?
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Which law of vector addition do vectors obey by definition?
Which law of vector addition do vectors obey by definition?
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What is the dimension of λA when a vector A is multiplied by a scalar λ with physical dimension?
What is the dimension of λA when a vector A is multiplied by a scalar λ with physical dimension?
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In the context of vector addition, what does the angle α represent?
In the context of vector addition, what does the angle α represent?
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What is the formula for calculating the magnitude of the resultant vector R in terms of vectors A and B?
What is the formula for calculating the magnitude of the resultant vector R in terms of vectors A and B?
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If PM represents a vector in direction specified by the problem, what does PM equal to?
If PM represents a vector in direction specified by the problem, what does PM equal to?
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For vector addition using the parallelogram method, what does SN represent in relation to the resultant vector R?
For vector addition using the parallelogram method, what does SN represent in relation to the resultant vector R?
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What type of triangle is used for calculating the magnitude of R using the Law of Cosines?
What type of triangle is used for calculating the magnitude of R using the Law of Cosines?
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In which direction is the resultant velocity of the boat calculated in the given example?
In which direction is the resultant velocity of the boat calculated in the given example?
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What is the relationship between velocity and acceleration in one dimension?
What is the relationship between velocity and acceleration in one dimension?
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For motion in two or three dimensions, what range of angles can exist between velocity and acceleration vectors?
For motion in two or three dimensions, what range of angles can exist between velocity and acceleration vectors?
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Given the position of a particle as r = 3.0t i + 2.0t^2 j + 5.0 k, what is the acceleration of the particle at any time t?
Given the position of a particle as r = 3.0t i + 2.0t^2 j + 5.0 k, what is the acceleration of the particle at any time t?
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If a particle's velocity at t = 1.0 s is v = 3.0 i + 4.0 j m/s, what is the magnitude of its velocity at that instant?
If a particle's velocity at t = 1.0 s is v = 3.0 i + 4.0 j m/s, what is the magnitude of its velocity at that instant?
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At t = 1.0 s, if a particle's velocity is v = 3.0 i + 4.0 j m/s, what is the direction of the velocity in relation to the x-axis?
At t = 1.0 s, if a particle's velocity is v = 3.0 i + 4.0 j m/s, what is the direction of the velocity in relation to the x-axis?
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What happens to the average acceleration over an interval of time when the acceleration of an object moving in the x-y plane is constant?
What happens to the average acceleration over an interval of time when the acceleration of an object moving in the x-y plane is constant?
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What is the direction θ that R makes with the vertical?
What is the direction θ that R makes with the vertical?
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How can a vector be resolved into two component vectors along a set of two vectors?
How can a vector be resolved into two component vectors along a set of two vectors?
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What is the purpose of a unit vector in a rectangular coordinate system?
What is the purpose of a unit vector in a rectangular coordinate system?
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How are unit vectors along the x-, y-, and z-axes denoted?
How are unit vectors along the x-, y-, and z-axes denoted?
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What is the magnitude of a unit vector?
What is the magnitude of a unit vector?
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What happens when a unit vector is multiplied by a scalar?
What happens when a unit vector is multiplied by a scalar?
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Study Notes
Scalars and Vectors
- Scalars can be multiplied and divided, but they do not have a fixed location.
- Vectors can be displaced parallel to themselves without changing, making them "free vectors".
- In some physical applications, the location or line of application of a vector is important, making them "localised vectors".
- Multiplying a vector by a scalar with a physical dimension changes the dimension of the resulting vector.
Addition and Subtraction of Vectors
- Vectors can be added and subtracted graphically using the parallelogram method.
- Two vectors are equal if and only if they have the same magnitude and direction.
Multiplication of Vectors by Real Numbers
- Multiplying a vector by a positive number changes its magnitude but not its direction.
- Vectors obey the triangle law or parallelogram law of addition.
Resolving Vectors
- A vector can be resolved into two component vectors along a set of two non-colinear vectors.
- Unit vectors are used to specify directions; they have no dimension or unit.
- Unit vectors along the x-, y-, and z-axes of a rectangular coordinate system are denoted by i, j, and k, respectively.
Vector Quantities
- A vector quantity has both magnitude and direction and obeys the triangle law of addition.
- Examples of vector quantities include displacement, velocity, acceleration, and force.
Displacement Vector
- A displacement vector is a vector that represents the motion of an object from one position to another.
- The magnitude of the displacement vector is the magnitude of the motion.
Resultant Vector
- The resultant vector is the sum of two or more vectors.
- The magnitude and direction of the resultant vector can be calculated using the parallelogram method.
Acceleration
- Acceleration is the rate of change of velocity.
- In one dimension, acceleration is always along the same straight line as velocity.
- In two or three dimensions, velocity and acceleration vectors may have any angle between 0° and 180°.
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Description
Test your knowledge on resolving vectors into component vectors and calculating directions in physics. Practice finding angles and components of vectors using given equations and figures.
