In a four dimensional space where unit vectors along axes are 
, 
, 
and 
and 
, 
, 
, 
are four non-zero vectors such that no vector can be expressed as linear combination of others and ( λ –1) ( 
– 
) + μ ( 
+ 
) + γ ( 
+ 
– 2 
) + 
+ δ 
= 
, then find the value of 3( λ + μ + γ + δ ).
Text Solution
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Ans. 1
Sol. ( λ –1) ( 
– 
) + μ ( 
+ 
) + γ ( 
+ 
– 2 
)
+ 
+ δ 
= 
i.e. ( λ –1) 
+ (1 – λ + μ –2 γ ) 
+ ( μ + γ + 1) 
+ ( γ + δ ) 
= 
Since 
, 
, 
, 
are linearly independent
∴λ –1= 0, 1 – λ + μ –2 γ = 0, μ + γ + 1 = 0, γ + δ = 0
i.e. λ = 1, μ = – 
, γ = – 
, δ = 
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