Calculus - Dot Product

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consider a rhombus ABCD
a) find the resultant of vector AB + vector AD and vector AB - vector AD? (cosine rule)
b) What will be the value of the dot product of vector AB + vector AD and vector AB - vector AD always be? (always zero)
c) Is this value of the dot product of vector AB - vector AD dot product vector AB + vector AD (commutative property)

Can someone please check if the answers in the brackets are correct!!!

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