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AP EAMCET201921 Apr 2019Morning ShiftMathematicsVector AlgebraActual

If 3 i -2 j - k , 2 i +3 j -4 k ,- i + j +2 k and 4 i +5 j + k are respectively the position vectors of four coplanar points P, Q, R and S , then =

Options

  1. A46 17
  2. B- 46 17
  3. C146 17
  4. D- 146 17

Correct answer

D. - 146 17

Step-by-step solution

Given, aligned & P =3 i -2 j - k & Q =2 i +3 j -4 k & R =- i + j +2 k aligned aligned & and S =4 i +5 j + k & Here, PS =(4-3) i +(5+2) j +( +1) k & = i +7 j +( +1) k & P Q =- i +5 j -3 k & and P R =-4 i +3 j +3 k & aligned Now, aligned P Q & P R = | array ccc i & j & k -1 & 5 & -3 -4 & 3 & 3 array | & = i (15+9)- j (-3-12)+ k (-3+20) & =24 i +15 j +17 k aligned Since, P, Q, R and S are coplanar, array lc & P S ( P Q P R )=0 & [ i +7 j +( +1) k ] [24 i +15 j +17 k ]=0 & 24+105+17( +1)=0 129+17 +17=0 & 17 =-146 =- 14

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