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Calculating Dot Product Using Components definitions

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  • Dot Product
    A scalar result from multiplying parallel components of two vectors and summing them.
  • Vector Components
    Parts of a vector described by unit vectors i, j, and k, representing dimensions.
  • Unit Vector
    A vector with a magnitude of one, used to indicate direction in space.
  • Scalar
    A single number resulting from operations like the dot product of vectors.
  • Parallel Components
    Parts of vectors that align in the same direction, used in dot product calculations.
  • Magnitude
    The length or size of a vector, used in calculating dot products with angles.
  • Angle
    The measure of rotation between two vectors, used in dot product calculations.
  • i, j, k
    Standard unit vectors representing the x, y, and z axes in 3D space.
  • Component-wise Multiplication
    Multiplying corresponding components of vectors to calculate the dot product.
  • Zero Component
    A placeholder for missing dimensions in vectors, treated as zero in calculations.