A parallelogram is construct 3a→+b→ and a→−4b→, where |a→|=6 and |b→|=8, and a→ and b→ are anti parallel. Then the length of the longer diagonal is

(3a→+b→)⋅(a→−4b→)=3|a→|2−11a→⋅b→−4|b→|2=3×36−11×6×8cos⁡π−4×64>0Therefore, the angle between a→ and b→ is acute. The longer diagonal is given by α→=(3a→+b→)+(a→−4b→)=4a→−3b→now, |α→|2=|4a→−3b→|2 =16|a→|2+9|b→|2−24a→⋅b→ =16×36+9×64−24×6×8cos⁡π =16×144or  |4a→−3b→|=48