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What is a position vector and what does it specify?
A position vector specifies the position of a point in space relative to an origin.
How is a position vector typically notated in a Cartesian coordinate system?
A position vector is often denoted as r and expressed in the form (x, y, z).
Define a displacement vector.
A displacement vector represents a change in position of a point from one location to another.
How do you calculate a displacement vector?
Displacement is calculated as Final Position - Initial Position.
Why do displacement vectors have both magnitude and direction?
Displacement vectors define movement with both size (how far) and direction (where to) from the initial to the final position.
What differentiates a position vector from a displacement vector?
Position vectors indicate location relative to a reference point, while displacement vectors indicate a change in position.
What is meant by vector addition being commutative?
Vector addition is commutative, meaning A + B = B + A.
How is vector subtraction visualized?
By reversing the direction of the vector being subtracted or subtracting a vector by adding its negative.
Explain what happens when a vector is multiplied by a scalar.
Multiplying a vector by a scalar changes the magnitude of the vector without altering its direction.
Why are vectors important in physics?
Vectors model various physical phenomena such as force, velocity, and acceleration, essential for describing motion.
How are vectors used in the context of motion and dynamics?
Vectors are used to describe both the position and movement aspects of motion through position and displacement.
What is a resultant vector in the context of vector operations?
The resultant vector is the vector obtained when vectors are added head-to-tail.
Describe the method for adding vectors.
Vectors are added by aligning them head-to-tail, drawing the resultant from the tail of the first to the head of the last.
In what scenario would a displacement vector be zero?
A displacement vector is zero if the final and initial positions are the same, indicating no change in position.
Can a scalar have negative values and how does it affect vector multiplication?
Yes, a scalar can be negative, which would reverse the direction of the resulting vector while scaling its magnitude.