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COMEDK2022MathematicsVector Algebra

If p = i + j , q =4 k - j and r = i + k , then the unit vector in the direction of 3 p + q -2 r is

Options

  1. A1 3 ( i +2 j +2 k )
  2. B1 3 ( i -2 j -2 k )
  3. C1 3 ( i -2 j +2 k )
  4. Di +2 j +2 k

Correct answer

A. 1 3 ( i +2 j +2 k )

Step-by-step solution

Given vectors are p = i + j , q = - j + 4 k , and r = i + k . Calculate the vector v = 3 p + q - 2 r : v = 3( i + j ) + (- j + 4 k ) - 2( i + k ) v = (3 i + 3 j ) + (- j + 4 k ) - (2 i + 2 k ) v = (3 - 2) i + (3 - 1) j + (4 - 2) k v = i + 2 j + 2 k The magnitude of vector v is | v | = 1^2 + 2^2 + 2^2 = 1 + 4 + 4 = 9 = 3 . The unit vector in the direction of v is u = v | v | = 1 3 ( i + 2 j + 2 k ) . Answer: 1 3 ( i +2 j +2 k )

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