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AP EAMCET2015MathematicsVector Algebra

If a =2 i + k , b = i + j + k , c =4 i -3 j +7 k , then the vector r satisfying r b=c b and r . a=0 is

Options

  1. Ai +8 j +2 k
  2. Bi -8 j +2 k
  3. Ci -8 j -2 k
  4. D-i -8 j +2 k

Correct answer

D. -i -8 j +2 k

Step-by-step solution

(d) Three vectors a , b and c are given as, a=2 i + k , b= i + j + k and c=4 i -3 j +7 k Given condition, r b = c b aligned & r b - c b =0 & ( r - c ) b =0 aligned It means, ( r - c ) | b So, r-c= b Also given, r a =0(c+ b) a=0 [using Eq. (i)] aligned & (4 i -3 j +7 k + i + j + k ) (2 i + k )=0 & [(4+ ) i +(-3+ ) j +(7+ ) k ] (2 i + k )=0 & (4+ ) 2+(7+ ) 1=0 & 8+2 +7+ =0 & 3 =-15 & =-5 aligned Put the value of in Eq. (i), we get aligned & r=4 i -3 j +7 k -5( i + j + k ) & =4 i -3 j +7 k -5 i -5 j -5 k =- i -8 j +2

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