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KCET2024MathematicsVector Algebra

The vectors A B =3 i +4 k and A C =5 i -2 j +4 k are the sides of a A B C , The length of the median through A is

Options

  1. A18
  2. B72
  3. C33
  4. D288

Correct answer

C. 33

Step-by-step solution

Let A = origin A B = Position vector of B A C = Position vector of C Position vector of mid-point of B and C = P = A B + A C 2 = ( 3+5 2 ) i + ( 0-2 2 ) j + ( 4+4 2 ) k =4 i - j +4 k Median = A P =4 i - j +4 k Hence, length of median =| A P |= 16+1+16 = 33

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