Let a = i +2 j +3 k and b = i -2 j -3 k be two vectors. If A₁ is the area of the quadrilateral having a , b as its diagonals and A₂ is the area of the parallelogram having a , b as its two adjacent sides, then A ₁ A ₂=

Step-by-step solution

a = i +2 j +3 k and b = i -2 j -3 k A₁= Area of the quadrilateral having a , b as diagonals A₁= 1 2 | a b | Now, a b = | array ccc i & j & k 1 & 2 & 3 1 & -2 & -3 array | aligned & = i (-6+6)- j (-3-3)+ k (-2-2) & =0 i +6 j -4 k & a b =6 j -4 k & | a b |= 36+16 = 52 aligned Then A₁= 1 2 52 Now, A₂= Area of parallelogram having a , b as its adjacent sides A₂=| a b |= 52 So, A₁ A₂= 1 2 52 52 = 52 2 =26 .