A parallelogram has its sides determined by vector OA=(5,1) and vector OB=(-1,4). Determine the angle between the two diagonals of this parallelogram.

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veca+vecb is one diagonal of the parallelogram.

veca-vecb is the other diagonal of the parallelogram.

`cos(theta)=(vecx*vecy)/(|vecx||vecy|)`

`vecx=veca+vecb=(4,5)`

`vecy=veca-vecb=(6,-3)`

`vecx*vecy=4*6+5*(-3)=24-15=9`

`|vecx|=sqrt(4^2+5^2)=sqrt(16+25)=sqrt(41)`

`|vecy|=sqrt(6^2+(-3)^2)=sqrt(36+9)=sqrt(45)`

`cos(theta)=(9)/(sqrt(41)sqrt(45))=9/(sqrt(41)(3sqrt(5)))`

`theta=cos^(-1)(3/(sqrt(41)(sqrt(5))))=77.9^o` our answer

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