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If | c |^2=60 and c ( i +2 j +5 k )= 0 , then a value of c (-7 i +2 j +3 k ) is:

Options

  1. A4 2
  2. B12
  3. C24
  4. D12 2

Correct answer

D. 12 2

Step-by-step solution

Let, c =a i +b j +c k Given, c ( i +2 j +5 k )= 0 aligned & | array ccc i & j & k a & b & c 1 & 2 & 5 array |= 0 & (5 b-2 c) i -(5 a-c) j +(2 a-b) k &=0 i +0 j +0 k aligned Comparing both sides, we get 5 b-2 c=0 ; 5 a-c=0 ; 2 a-b=0 or 5 b=2 c ; 5 a=c ; 2 a=b Also given | c |^2=60 a^2+b^2+c^2=60 Putting the value of b and c in above eqn., we get aligned &a^2+(2 a)^2+(5 a)^2=60 & a^2+4 a^2+25 a^2=60 30 a^2=60 &a^2=2 &a= 2 ; b=2 2 ; c=5 2 aligned Now, c =a i +b j +c k c = 2 i +2 2 j +5 2 k Value of c (-7 i +2 j +3 k )

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