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Question

In a four dimensional space, where unit vectors along the axes are ^i,^j,^k and ^l,a1,a2,a3,a4 are four non-zero vectors such that no vector can be expressed as a linear combination of others and (λ1)(a1a2)+α(a2+a3)+γ(a3+a42a2)+a3+δa4=0.
Then which of the following is/are correct?

A
λ=1
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B
α=2
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C
γ=1
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D
δ=13
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Solution

The correct option is D δ=13
Here, (λ1)(a1a2)+α(a2+a3)+γ(a3+a42a2)+a3+δa4=0

(λ1)a1+(1λ+α2γ)a2 +(α+γ+1)a3+(γ+δ)a4=0
Since a1,a2,a3,a4 are linearly independent, therefore
λ1=0,
1λ+α2γ=0,
α+γ+1=0,
and γ+δ=0

On solving above equations, we get
λ=1
α=23
γ=13
δ=13







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