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Questions and Answers
What is the direction angle of a vector 𝐴 = 10.0 N, 30.0° N of E?
What is the direction angle of a vector 𝐴 = 10.0 N, 30.0° N of E?
- 60.0° E of N (correct)
- 30.0° W of N
- 60.0° W of N
- 30.0° E of N
When determining the correct direction angle, what should you start with?
When determining the correct direction angle, what should you start with?
- The components of the vector
- Trigonometric relations
- Calculations
- A vector diagram (correct)
What is the direction of the vector 𝐴 = 10.0 N, 60.0° E of N?
What is the direction of the vector 𝐴 = 10.0 N, 60.0° E of N?
- North of East (correct)
- South of East
- West of North
- East of North
How do you measure the direction angle in the first quadrant?
How do you measure the direction angle in the first quadrant?
What is the direction of the vector 𝐴 = 10.0 N, 30.0° W of N?
What is the direction of the vector 𝐴 = 10.0 N, 30.0° W of N?
How do you measure the direction angle in the second quadrant?
How do you measure the direction angle in the second quadrant?
What is the direction of the vector 𝐴 = 10.0 N, 30.0° E of S?
What is the direction of the vector 𝐴 = 10.0 N, 30.0° E of S?
What is the x-component of vector A in terms of its magnitude and angle θ?
What is the x-component of vector A in terms of its magnitude and angle θ?
What is the significance of examining the signs of the components of the vector?
What is the significance of examining the signs of the components of the vector?
In which quadrant would a vector have a positive x-component and a negative y-component?
In which quadrant would a vector have a positive x-component and a negative y-component?
What is the y-component of vector A in terms of its magnitude and angle ϕ?
What is the y-component of vector A in terms of its magnitude and angle ϕ?
If the x-component of a vector is negative, in which quadrant would it lie?
If the x-component of a vector is negative, in which quadrant would it lie?
What is the relationship between the magnitude of a vector and its components?
What is the relationship between the magnitude of a vector and its components?
What is the direction of the angle measured from the +x-axis?
What is the direction of the angle measured from the +x-axis?
What is the y-component of vector A in terms of its magnitude and angle θ?
What is the y-component of vector A in terms of its magnitude and angle θ?
What is the value of the x-component of vector A?
What is the value of the x-component of vector A?
What is the magnitude of vector A?
What is the magnitude of vector A?
What is the purpose of the unit vector of a vector?
What is the purpose of the unit vector of a vector?
What is the magnitude of the unit vector?
What is the magnitude of the unit vector?
What is the result of dividing the perpendicular component of a vector by its magnitude?
What is the result of dividing the perpendicular component of a vector by its magnitude?
What is the formula for the unit vector?
What is the formula for the unit vector?
What is the unit vector for the x-coordinate?
What is the unit vector for the x-coordinate?
What is the relationship between the magnitude of a vector and its unit vector?
What is the relationship between the magnitude of a vector and its unit vector?
Which of the following is NOT a correct way to write the component vector of A in the x-direction?
Which of the following is NOT a correct way to write the component vector of A in the x-direction?
What is the full decomposition of the vector A?
What is the full decomposition of the vector A?
In a 3D rectangular coordinate system, which unit vector is along the x-axis?
In a 3D rectangular coordinate system, which unit vector is along the x-axis?
What is the purpose of unit vectors in decomposing a vector?
What is the purpose of unit vectors in decomposing a vector?
Which of the following is a correct way to write the y-component of a vector?
Which of the following is a correct way to write the y-component of a vector?
What is a characteristic of a scalar quantity?
What is a characteristic of a scalar quantity?
What is an example of a vector quantity?
What is an example of a vector quantity?
What is the equation for the magnitude of a vector 𝐴⃗?
What is the equation for the magnitude of a vector 𝐴⃗?
How is a vector quantity represented in analytic form?
How is a vector quantity represented in analytic form?
What determines the component form of a vector representation?
What determines the component form of a vector representation?
What is the symbol used to represent a vector quantity?
What is the symbol used to represent a vector quantity?
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Study Notes
Scalar and Vector
- Scalars are quantities that can be described by a magnitude (or number and units) alone, such as speed, mass, and temperature.
- Vectors are quantities that can be completely described by both a magnitude and a direction in space, such as displacement, velocity, and force.
Vector Representations
- Vectors can be represented in magnitude-direction form: A⃗ = Aa,whereAisthemagnitudeanda, where A is the magnitude and a,whereAisthemagnitudeanda is the direction.
- Vectors can also be represented in component form: A⃗ = Ax + Ay + Az, where Ax, Ay, and Az are the components of the vector in the x, y, and z directions.
Unit Vectors
- A unit vector or normalized vector of a vector is defined as: a@ ≡ A / |A|, where A is the magnitude of the vector.
- The unit vector has a magnitude of 1 and indicates only the direction of a vector.
Components of a Vector
- The x-component of a vector A is given by: Ax = Acos θ (with respect to the x-axis).
- The y-component of a vector A is given by: Ay = Asin θ (with respect to the y-axis).
Decomposition of a 2D Vector
- When decomposing a vector, unit vectors provide a useful way to write component vectors.
- The decomposition of a 2D vector A can be written as: A = Ax ı̂ + Ay ȷ̂, where Ax and Ay are the x and y components of the vector, and ı̂ and ȷ̂ are the unit vectors in the x and y directions.
Decomposition of a 3D Vector
- In a 3D rectangular coordinate system, a vector A can be decomposed into three components: Ax, Ay, and Az, along the x, y, and z axes.
- The full decomposition of a 3D vector A can be written as: A = Ax ı̂ + Ay ȷ̂ + Az ̂, where Ax, Ay, and Az are the x, y, and z components of the vector, and ı̂, ȷ̂, and ̂ are the unit vectors in the x, y, and z directions.
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