If the area of the parallelogram whose adjacent sides are (3^i−4^j+λ^k) and (2^j−4^k) is √436 sq. units and λ>0, then λ is
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Solution
Area of parallelogram =|→a×→b|
Area of parallelogram =|(3^i−4^j+λ^k)×(2^j−4^k)| ⇒|(16−2λ)^i+12^j+6^k|=√436 ⇒√(16−2λ)2+122+62=√436
Squaring both sides ⇒(16−2λ)2+144+36=436 ⇒(16−2λ)2=256 ⇒(16−2λ)=±16 ⇒λ=0,16