ABCD IS QUADRILATERAL WITH AB =X AD = b AC =2a+3b if area is X times the - Maths - Vector Algebra

Question

ABCD IS QUADRILATERAL WITH AB =X AD = b & AC =2a+3b if area is
X times the area of parallrlogramwith AB ,AD AS ADJACENT SIDES THEN
X IS

Manbar Singh · Accepted Answer

We have :AB→ = a→; AD→ = b→; AC→ = 2a→ + 3b→Now, area of quadrilateral ABCD = area of ∆ABC +  area of ∆ACD=12AB→ × AC→ + 12AC→ ×AD→=12a→×2a→ + 3b→ + 122a→ + 3b→×b→=122a→×a→ + 3a→×b→ + 122a→×b→ + 3b→×b→=120→ + 3a→×b→ + 122a→×b→ + 0→=123a→×b→ + 2a→×b→=52a→×b→=52AB→×AD→=52area of ∥gm ABCDSo, x = 52

ABCD IS QUADRILATERAL WITH AB =X AD = b & AC =2a+3b. if area is X times the area of parallrlogramwith AB ,AD AS ADJACENT SIDES THEN X IS