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AP EAMCET2007MathematicsVector Algebra

If the points whose position vectors are 2 i + j + k , 6 i - j +2 k and 14 i -5 j +p k are collinear, then the value of p is are collinear, then the value of p is

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

B. 4

Step-by-step solution

Given vectors a =2 i + j + k , b =6 i - j +2 k and c =14 i -5 j +p k are collinear, therefore [ a b c ]=0 array cccc & & | array ccc 2 & 1 & 1 6 & -1 & 2 14 & -5 & p array |=0 & 2[-p+10]-1[6 p-28]+1[-30+14]=0 & -2 p+20-6 p+28-16=0 & & -8 p+32=0 & & p=4 array

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