Podcast
Questions and Answers
What does the position vector 𝑟⃗ (𝑡) represent in a three-dimensional Cartesian coordinate system?
What does the position vector 𝑟⃗ (𝑡) represent in a three-dimensional Cartesian coordinate system?
Which of the following correctly describes displacement?
Which of the following correctly describes displacement?
How can the displacement vector 𝛥𝑟⃗ be expressed using unit-vector notation?
How can the displacement vector 𝛥𝑟⃗ be expressed using unit-vector notation?
What is the correct representation of a position vector of point P with coordinates (-3, 2, 5)?
What is the correct representation of a position vector of point P with coordinates (-3, 2, 5)?
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Which term symbolizes the change in position of an object?
Which term symbolizes the change in position of an object?
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In the context of position vectors, what does the origin refer to?
In the context of position vectors, what does the origin refer to?
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What happens to the position vector when an object's coordinates change?
What happens to the position vector when an object's coordinates change?
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Which statement is true regarding the components of a position vector?
Which statement is true regarding the components of a position vector?
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Study Notes
Position Vector
- Defines the location of a point in space relative to a fixed reference point called the origin.
- Represented as a vector, denoted by 𝑟⃗.
- The position is a function of time, expressed as 𝑟⃗(𝑡).
- In a three-dimensional Cartesian coordinate system (x, y, z), the position vector for point P(x, y, z) relative to the origin O(0, 0, 0) is given by:
- 𝑟⃗ = 𝑥𝑖̇̂ + 𝑦𝑗̇̂ + 𝑧𝑘̂
- Example of a position vector: 𝑟⃗ = (−3𝑚)𝑖̇̂ + (2𝑚)𝑗̇̂ + (5𝑚)𝑘̂.
Displacement
- Defined as the change in position of an object from an initial position to a final position.
- Measures the relative change in position concerning a reference point.
- It is a vector quantity, indicating both magnitude and direction.
- Represented by the symbol 𝛥𝑟⃗.
- Displacement is calculated as:
- ∆𝑟⃗ = 𝑟⃗2 − 𝑟⃗1
- In unit-vector notation:
- ∆𝑟⃗ = (𝑥2𝑖̇̂ + 𝑦2𝑗̇̂ + 𝑧2𝑘̂) − (𝑥1𝑖̇̂ + 𝑦1𝑗̇̂ + 𝑧1𝑘̂)
- Simplified to: ∆𝑟⃗ = (𝑥2 − 𝑥1)𝑖̇̂ + (𝑦2 − 𝑦1)𝑗̇̂ + (𝑧2 − 𝑧1)𝑘̂
- Also expressed as ∆𝑟⃗ = ∆𝑥𝑖̇̂ + ∆𝑦𝑗̇̂ + ∆𝑧𝑘̂.
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Description
This quiz covers the concepts of position vectors and displacement in physics. Learn how to represent and calculate both vector quantities in a three-dimensional space. Understand the significance of the origin and the change in position relative to it.
