# Answer to Question #12458 in Analytic Geometry for john.george.milnor

Question #12458

Prove identity: [a,b]^2+(a,b)^2=|a|^2 * |b|^2, where a and b are vectors

Expert's answer

|[a,b]|=|a|*|b|*sin(a^b)

(a,b)=|a|*|b|*cos(a^b)

Using cos^2(x)+sin^2(x)=1

and squaring two previuos equalities we obtain

necessary result.

(a,b)=|a|*|b|*cos(a^b)

Using cos^2(x)+sin^2(x)=1

and squaring two previuos equalities we obtain

necessary result.

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