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JEE Main2012MathematicsVector AlgebraActual

Let A B C D be a parallelogram such that A B = q , A D = p and B A D be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side A D , then r is given by

Options

  1. Ar =3 q - 3( p q ) ( p p ) p
  2. Br =- q + ( p q p p ) p
  3. Cr = q - ( p q p p ) p
  4. Dr =-3 q + 3( p q ) ( p p ) p

Correct answer

B. r =- q + ( p q p p ) p

Step-by-step solution

AE = vector component of q on p AE = ( p q ) ( p q ) p From ABE ; AB + BE = AE q + r = ( p q ) p ( p q ) r =- q + ( p q ) ( p p ) p

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