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AP EAMCET202120 Aug 2021Morning ShiftMathematicsVector AlgebraActual

Let u → = 2 i ^ + 3 j ^ + k ^ , v → = - 3 i ^ + 2 j ^ and w → = i ^ - j ^ + 4 k ^ , Then which of the following statement is true?

Options

  1. Au → is perpendicular to v → but not w →
  2. Bv → is perpendicular to w → but not u →
  3. Cw → is perpendicular to u → but not v →
  4. Du → is perpendicular to both v → and w →

Correct answer

A. u → is perpendicular to v → but not w →

Step-by-step solution

u → = 2 i ^ + 3 j ^ + k ^ ,   v → = - 3 i ^ + 2 j ^ , w → = i ^ - j ^ + 4 k ^ u → . v → = 2 i ^ + 3 j ^ + k ^ . - 3 i ^ + 2 j ^ ⇒ u → . v → = - 6 + 6 + 0 ⇒ u → . v → = 0   Therefore. u → is perpendicular to v → . Now, u → . w → = ( 2 i ^ . i ^ ) + ( 3 j ^ . - j ^ ) + ( k ^ . 4 k ^ ) ⇒ u → . w → = 2 - 3 + 4 = 3 Therefore, u → is not perpendicular w → . Now, w → . v → = i ^ - j

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