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Vectors in Component Form quiz

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  • What is a position vector and how is it represented in component form?
    A position vector has its initial point at the origin and is represented in component form as (x, y), where x and y are the horizontal and vertical components.
  • How do you find the component form of a vector given its initial and terminal points?
    Subtract the initial coordinates from the terminal coordinates: (x2 - x1, y2 - y1).
  • What do the x and y components of a vector in component form represent?
    They represent how far the vector moves in the x (horizontal) and y (vertical) directions.
  • How do you calculate the magnitude of a vector in component form (x, y)?
    Use the formula magnitude = √(x² + y²), which is based on the Pythagorean theorem.
  • If a vector has components (4, 3), what is its magnitude?
    The magnitude is √(4² + 3²) = √(16 + 9) = √25 = 5.
  • How do you add two vectors in component form?
    Add their corresponding x components and y components: (x1 + x2, y1 + y2).
  • How do you subtract one vector from another in component form?
    Subtract their corresponding x and y components: (x1 - x2, y1 - y2).
  • What is the result of adding vectors (2, 3) and (3, -1)?
    The sum is (2 + 3, 3 + (-1)) = (5, 2).
  • How do you multiply a vector by a scalar?
    Multiply each component of the vector by the scalar: k(x, y) = (kx, ky).
  • What is the component form of 3 times the vector (2, 4)?
    It is (3 × 2, 3 × 4) = (6, 12).
  • Given vectors v = (8, 5) and u = (2, 4), what is v - 3u?
    First, 3u = (6, 12), then v - 3u = (8 - 6, 5 - 12) = (2, -7).
  • If a vector has initial point (1, 2) and terminal point (5, 3), what is its component form?
    The component form is (5 - 1, 3 - 2) = (4, 1).
  • How do you find the magnitude of a vector given its initial and terminal points?
    First, find the component form by subtracting coordinates, then use magnitude = √(x² + y²).
  • Why is the Pythagorean theorem used to find the magnitude of a vector?
    Because the x and y components form a right triangle, and the vector's magnitude is the hypotenuse.
  • What is the general process for performing vector operations in component form?
    Add, subtract, or multiply the x and y components as required by the operation.