Vectors and scalers
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Questions and Answers

What is a characteristic of a scalar quantity?

  • It can be represented graphically using arrows
  • It can be subtracted by adding the negative of one scalar to another
  • It has both magnitude and direction
  • It has only magnitude but no direction (correct)

    • Which of the following is an example of a vector?

  • Speed
  • Displacement (correct)
  • Energy
  • Mass

    • How can vectors be added?

  • By combining their magnitudes
  • By combining their corresponding components (correct)
  • By multiplying their magnitudes
  • By subtracting their corresponding components

    • What is the result of multiplying a vector by a number?

    <p>The magnitude of the vector changes but not its direction</p> Signup and view all the answers

    What notation is used to represent the magnitude of a vector?

    <p>||</p> Signup and view all the answers

    What is a property of vector addition?

    <p>Commutative Property</p> Signup and view all the answers

    Study Notes

    Scalars and Vectors

    Scalars

    • A scalar is a quantity with only magnitude (amount or size) but no direction.
    • Examples: temperature, mass, time, energy, speed
    • Scalars can be added or subtracted by simple arithmetic operations.
    • Scalars can be multiplied or divided by numbers.

    Vectors

    • A vector is a quantity with both magnitude (amount or size) and direction.
    • Examples: displacement, velocity, acceleration, force, momentum
    • Vectors can be represented graphically using arrows in a coordinate system.
    • Vectors have both magnitude (length of the arrow) and direction (direction of the arrow).

    Vector Operations

    • Addition: Vectors can be added by combining their corresponding components.
    • Scalar Multiplication: A vector can be multiplied by a number, which changes its magnitude but not its direction.
    • Vector Subtraction: Vectors can be subtracted by adding the negative of one vector to another.

    Vector Notation

    • Column Notation: Vectors can be represented as columns of numbers, e.g. |a| |b|
    • Magnitude: The magnitude of a vector can be represented using the symbol | | or ||, e.g. |a|
    • Unit Vectors: Vectors with a magnitude of 1, used to represent direction, e.g. i, j, k

    Vector Properties

    • Commutative Property: The order of vectors does not change the result of addition, e.g. a + b = b + a
    • Associative Property: The order in which vectors are added does not change the result, e.g. (a + b) + c = a + (b + c)
    • Distributive Property: A scalar can be distributed to each component of a vector, e.g. a(b + c) = ab + ac

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