School of Mathematics and Statistics, The University of Sydney
 9. The scalar product
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Conditions for perpendicularity

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By definition of the scalar product, u·v = |u||v| cos h, where h is the angle between u and v. If h = 90° then cos h = 0. Given two non-zero vectors u and v

u and v are perpendicular if and only if u · v = 0.

If u = u1i + u2j + u3k and v = v1i + v2j + v3k are given in Cartesian form then the above reads

u and v are perpendicular if and only if u1v1 + u2v2 + u3v3 = 0.

For vectors in the plane drop the third terms.

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Main menu Section menu   Previous section Next section Algebraic rules The scalar product of the standard basis vectors