<prompt> Sambamba hutokezwa na vekta beginpmatrix 2 1 1 endpmatrix na beginpmatrix 1 -1 - 1 endpmatrix.asyukubwa wa kitengo sentimita 0.4;jozi A, B, C, D;A 0,0;B 7,2;C 1,3;D B C;choraA--B,Arrow6;choraA--C,Arrow6;kuchoraB--D--C;kuchoraB--C,dashed;kuchoraA--D,dashed;asyIkiwa theta ni pembe kati ya diagonals, basi pata cos theta.  <response>: Tuseme kwamba vekta mathbfa na mathbfb zitoe paralelogramu. Kisha vekta zinazolingana na diagonals ni mathbfa mathbfb na mathbfb - mathbfa.asyukubwa wa kitengo sentimita 0.4;jozi A, B, C, D, trans;A 0,0;B 7,2;C 1,3;D B C;trans 10,0;kuchoraB--D--C;choraA--B,Arrow6;choraA--C,Arrow6;choraA--D,Arrow6;lebomathbfa, A B2, SE;lebomathbfb, A C2, W;lebomathbfa mathbfb, interpA,D,0.7, NW, UnFill;kuchorakuhamatransB--D--C;chorashifttransA--B,Arrow6;chorashifttransA--C,Arrow6;chorashifttransB--C,Arrow6;lebomathbfa, A B2 trans, SE;lebomathbfb, A C2 trans, W;lebomathbfb - mathbfa, B C2 trans, N;asyKwa hivyo, vekta zinazolingana na diagonals ni beginpmatrix 3 0 0 endpmatrix na beginpmatrix 1 2 2 endpmatrix. Kishacos theta fracanzapmatrix 3 0 0 mwishopmatrix cdot anzapmatrix 1 2 2 mwishopmatrixkushoto anzapmatrix 3 0 0 mwishopmatrix kulia kushoto anzapmatrix 1 2 2 mwishopmatrix kulia frac33 cdot 3 frac13. 