Physics Position and Displacement Vectors

What does the position vector 𝑟⃗ (𝑡) represent in a three-dimensional Cartesian coordinate system?

Which of the following correctly describes displacement?

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)?

Which term symbolizes the change in position of an object?

In the context of position vectors, what does the origin refer to?

What happens to the position vector when an object's coordinates change?

Which statement is true regarding the components of a position vector?

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.

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.