Vector Operations Calculator

Key formulas

• $$|\vec{a}| = \sqrt{a_x^{2} + a_y^{2}}$$

  Magnitude of a vector

  $|\vec{a}|$

  Magnitude

  $a_x$

  x component

  $a_y$

  y component

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• $$\vec{a} + \vec{b} = (a_x + b_x,\; a_y + b_y)$$

  Sum of two vectors

  $\vec{a}$

  First vector

  $\vec{b}$

  Second vector

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• $$\vec{a}\cdot\vec{b} = a_x b_x + a_y b_y = |\vec{a}||\vec{b}|\cos\theta$$

  Dot product

  $\vec{a}\cdot\vec{b}$

  Dot product

  $|\vec{a}|$

  Magnitude of a

  $|\vec{b}|$

  Magnitude of b

  $\theta$

  Angle between them°

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