If the area of parallelogram, whose diagonals are i - j +2 k and 2 i +3 j + k is 93 2 sq. unit, then =

Step-by-step solution

Given the diagonals of the parallelogram d₁ = i - j + 2 k and d₂ = 2 i + 3 j + k , the area is determined by the formula Area = 1 2 | d₁ d₂ | . The cross product evaluates to d₁ d₂ = (- - 6) i - ( - 4) j + 5 k . Its magnitude is | d₁ d₂ | = ( + 6)^2 + ( - 4)^2 + 25 = 2 ^2 + 4 + 77 . Given the area 93 2 , we have 1 2 2 ^2 + 4 + 77 = 93 2 , which simplifies to 2 ^2 + 4 + 77 = 93 . Squaring both sides yields 2 ^2 + 4 + 77 = 93 , leading to 2 ^2 + 4 - 16 = 0 . Dividing by 2 gives ^2 + 2 - 8 = 0 , which factors as ( + 4