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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Paragraph: Read the following write up carefully and answer the following questions: Let OP ₁ , OP ₂ , OP ₃ , ., OP _n be unit vectors in a plane. P ₁, P ₂, P ₃, . P _ n all lie on the same side of a line through O .| OM | denotes length of vector through O Question: If S = OP ₂ + OP ₃ + OP ₄ + OP ₅ + OP ₆ and V = OP ₁ + OP ₇ then least value of | S |+| V | is

Options

  1. A0
  2. B2
  3. C1
  4. Dnone of these

Correct answer

C. 1

Step-by-step solution

Here, P_ v = P ₂ + P _ k so P _ v will make acute angle with all the vectors from P ₂ , P ₃ , ., P _ k So, OP _ v ( OP ₂ + OP ₃ + .+ OP _ k -1 ) 0 Again, if n is odd n=2 k-1 OP ₁ + OP _ 2 k -1 = OP _ k Now OP _ k will make acute angle with all the vectors from OP ₁ , OP ₂ . . OP _ 2 k -1 OP _ k ( OP ₁ + OP ₂ + .+ OP _ k + OP _ k +1 + .+ OP _ 2 k -1 ) OP _ k OP _ k =1 Now, OP _ k ( OP ₁ + OP ₂ + .+ OP _ 2 k-1 ) | OP _ k | | OP ₁ + .+ OP _ 2 k-1 |= | OP ₁ + OP ₂ + . .+ OP _n | Again, V makes acute angle with all the

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