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Question

If the volume of a parallelopiped formed by the vectors ^i+λ^j+^k, ^j+λ^k and λ^i+^k is minimum, then λ is equal to :

A
13
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B
3
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C
13
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D
3
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Solution

The correct option is C 13
Volume of parallelopiped
=∣ ∣1λ101λλ01∣ ∣=1[10]λ[0λ2]+1[0λ]
V=|1+λ3λ|
dVdλ=3λ21=0
λ=±13
d2Vdλ2=6λ
For minimum V d2Vdλ2>0 which is at λ=13

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