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Question

If the area of the parallelogram whose adjacent sides are (3^i4^j+λ^k) and (2^j4^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^i4^j+λ^k)×(2^j4^k)|
|(162λ)^i+12^j+6^k|=436
(162λ)2+122+62=436
Squaring both sides
(162λ)2+144+36=436
(162λ)2=256
(162λ)=±16
λ=0,16

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