NIMCET 2020 Question Paper with solutions

Question : 37 of 120

Marks: +1, -0

If the volume of a parallelopiped whose adjacent edges are

a =2i+3j+4k,

b = i+ aj+ 2k,

c = i+ 2j+ ak

is 15, then α =

Solution:

Volume of parallelepiped

=[a b c]

According to the question

|\table 2,3,4;1,a,2;1,2,a|=15

2(α^2-4)-3(α-2)+4(2-α)=15

2α^2-7α+6=15

2α^2-7α-9=0

2α^2+2α-9α-9=0

2α(α+1)-9(α+1)=0

(α+1)(2α-9)

α=9/2,-1

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