Mathematics · University
Scalar coefficient in an orthogonal projection · formula reference
The coefficient multiplying u differs from the scalar projection onto the unit vector u/||u||.
Formula
The coefficient multiplying u differs from the scalar projection onto the unit vector u/||u||.
projᵤ(v) = [(v·u)/(u·u)]u
Worked example
Let v = (6,-9) and u = (1,8). Write the orthogonal projection of v onto span(u) as k u. Find k. Round the final result to 4 decimal places if needed.
Use k = (v·u)/(u·u) = (-66)/(65).
-1.0154
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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