Practice question · Multiple choice
The dot product of two perpendicular vectors is zero. Why is zero the natural signal for a right angle rather than some other special value?
Hints
- Project one vector onto the other. How long is the shadow at 90°?
- Ask what the dot product is measuring, then what that quantity is for perpendicular arrows.
Show the answer
C. Because at 90° neither vector has any component along the other
Why
The dot product prices alignment, and perpendicular vectors have none, the shadow of one on the other has zero length. That is why orthogonality is such a computational gift: an inner product of zero means the two directions carry genuinely independent information, which is what makes Fourier analysis and least squares work.
Practise Dot Product and Angles
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