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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Paragraph: Consider the three vectors p , q and r such that p = i + j + k ; q = i - j + k ; p r = q +c p and p r =2 Question: The value of [ p q r ] is

Options

  1. A- 5 2 c | r |
  2. B- 8 3
  3. C0
  4. DGreater then zero

Correct answer

B. - 8 3

Step-by-step solution

(i) Given p = i + j + k aligned & q = i - j + k & p r = q + c p and p r =2 aligned cross with p dot with p aligned & p ( p r )= p ( q + c p ) and p ( p r )= p ( q + c p ) aligned ( p r ) p -( p p ) r = p q + c 0 0= p q + c ( p p ) ( p p ) r =( p r ) p - p q ... (i) c=- p q p p ... (ii) But p p =| p |= p ^2=3 ... (iii) p q =1-1+1=1 ... (iv) p q = | array ccc i & j & k 1 & 1 & 1 1 & -1 & 1 array |=2 i -2 k ... (v) Using (iii), (iv), (v) in (i) and (ii), we get 3 r =2 p -2 i +2 k and c =- 1 3 ... (vii) r = 1 3 [2 i +2

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