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MHT CET20249 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

Let a = i +3 j - k , b =3 i - j +4 k and c = i +2 j -2 k , where , R , be three vectors. If the projection at a on c is 10 3 and b c =-6 i +10 j +7 k , then the value of ^2+ ^2- is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

Projection of a on c is 10 3 aligned & a c | c | = 10 3 & ( i +3 j - k ) ( i +2 j -2 k ) 1+4+4 = 10 3 & +3(2)-1(-2) 9 = 10 3 & +8 3 = 10 3 & =2 & ~b c =-6 i +10 j +7 k & | array cc i & j k 3 & - 1 & 2 array -2 |=-6 i +10 j +7 k & (2 -8) i +10 j +(6+ ) k =-6 i +10 j +7 k & 6+ =7 =1 & ^2+ ^2- =4+1-2=3 aligned

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