Projection of A onto B Calculator

Published on: March 22, 2026
Final Answer: Free • Full Steps: Pro

This Projection of A onto B Calculator helps you find the vector projection of one 3D vector onto another. First find the dot product of A and B, then divide by the magnitude squared of B to get the scalar factor. Multiply vector B by that factor to get the final projection vector. It is a simple way to check answers, understand the method clearly, and practise vector operations step by step.

Step-by-step method

  1. Identify the vector components.
  2. Compute the dot product A · B.
  3. Compute |B|².
  4. Use proj_B(A) = ((A · B) / |B|²) B and simplify.

Formula:

\(\operatorname{proj}_{\vec{B}} \vec{A} = \frac{\vec{A} \cdot \vec{B}}{\left|\vec{B}\right|^{2}} \, \vec{B}\)