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BITSAT2021MathematicsVector AlgebraActual

If a is a vector of magnitude 50 , collinear with the vector b =6 i -8 j - 15 2 k and makes an acute angle with the positive direction of Z - axis, then a is equal to

Options

  1. A-24 i +32 j +30 k
  2. B24 i -32 j -30 k
  3. C-12 i +16 j -15 k
  4. D12 i -16 j -15 k

Correct answer

A. -24 i +32 j +30 k

Step-by-step solution

Since a =m b for some scalar m i.e., array l a =m (6 i -8 j - 15 2 k ) |a|=|m| 36+64+ 225 4 50= 25 2 |m| |m|=4 m= 4 array Since, a makes an acute angle with the positive direction of Z - axis, so its z component must be positive and hence, m must be -4 . a=-4 (6 i +8 j - 15 2 k )=-24 i +32 j +30 k

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