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AP EAMCET2016MathematicsThree Dimensional Geometry

For three vectors p , q and r , if r =3 p +4 q and 2 r = p -3 q , then

Options

  1. A| r | < 2| q | and r , q have the same direction
  2. B| r |>2| q | and r , q have opposite directions
  3. C| r | < 2| q | and r , q have opposite directions
  4. D| r |>2| q | and r , q have the same direction

Correct answer

B. | r |>2| q | and r , q have opposite directions

Step-by-step solution

For three vectors p, q and r From eqs. (i) and (ii), we get aligned & r=3(2 r+3 q)+4 q & r=6 r+9 q+4 q & 5 r=-13 q r= 13 5 q |r|= 13 5 |q| aligned r and q have opposite directions Hence, |r|>2|q|

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