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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

In a four - dimensional space where unit vectors along axes are i , j , k and and a ₁, a ₂, a ₃, a ₄ are four non-zero vectors such that no vector can be expressed as linear combination of others and ( -1) ( a ₁- a ₂ )+ ( a ₂+ a ₃ )+ ( a ₃+ a ₄-2 a ₂ )+ a ₃+ a ₄= o then

Options

  1. A=1
  2. B=- 2 3
  3. C= 2 3
  4. D= 1 3

Correct answer

D. = 1 3

Step-by-step solution

( -1) ( a ₁- a ₂ )+ ( a ₂+ a ₃ )+ ( a ₃+ a ₄-2 a ₂ )+ a ₃+ a ₄= o i.e. ( -1) a ₁+(1- + -2 ) a ₂+( + +1) a ₃+( + ) a ₄= o Since a ₁, a ₂, a ₃, a ₄ are linearly independent aligned & =1=0,1- + -2 =0, + +1=0, + =0 & i.e. =1, =2 , + +1=0, + =0 & i.e. =1, =- 2 3 , =- 1 3 , = 1 3 aligned

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