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Introduction to 3D Vectors

Mathematics Grade 10 Difficulty 3/5

Beginning of the lesson

Introduction to 3D Vectors

What is a 3D Vector?

A vector is a mathematical object that has both magnitude (length) and direction. In three-dimensional space, vectors allow us to describe positions, movements, forces, and velocities in our physical world.

A 3D vector is typically represented in component form as:

v→=⟨vx,vy,vz⟩

or equivalently: v = vxi + vyj + vzk

where vx, vy, and vz are the components along the x, y, and z axes respectively, and i, j, k are the unit vectors in those directions.

Visualizing 3D Vectors

Vectors are represented as arrows in space, where:

  • The length of the arrow represents the magnitude
  • The direction of the arrow shows the vector's direction
  • The tail is typically at the origin (0, 0, 0) for position vectors
Mathematical diagram

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  • Test questions: 15
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