Vector components - Scalars, Vectors and Motion

Vector components



In this lesson, we will learn:

  • What are x and y components?
  • How to break a vector into its components
  • Problem solving with vector components


  • Components of a vector are other vectors that add up tip-to-tail give you the original vector.
    • The x and y components of a vector are the components that are pointed directly in the x and y directions, respectively, and are useful for solving problems.
    • The x and y components can be found with trigonometry, since they always form a right triangle with the original vector.
Right Triangle Trigonometric Equations

sin(θ)=opp.hyp.\sin(\theta) = \frac{opp.}{hyp.}

cos(θ)=adj.hyp.\cos(\theta) = \frac{adj.}{hyp.}

tan(θ)=opp.adj.\tan(\theta) = \frac{opp.}{adj.}

a2+b2=c2a^{2}+b^{2}=c^{2} (Pythagorean theorem)

θ\theta: angle, in degrees (°)

opp.opp.: side opposite angle

adj.adj.: side adjacent angle

hyp.hyp.: hypotenuse of triangle (longest side, side opposite 90° angle)

aa and bb: non-hypotenuse sides of triangle

cc: hypotenuse of triangle

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Vector components

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