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In vector multiplication we know that i×j=k and j×k=i and similarly k×i=j , i would like to know that will this property be valid for a×b=c and similarly

b×c=a and c×a=b with specified condition that the angle is 90 degrees??

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According to me the property cannot be applicable in case of these terms.According to pythagorean theorem,a^2 + b^2 = c^2 . so, c = sqrt{a^2 + b^2}. a = sqrt{c^2 - b^2} b = sqrt{c^2 - a^2} Subsituting these values in your equation a*b=c doesn't give equilibrium answer.