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AP EAMCET2009MathematicsThree Dimensional Geometry

In a quadrilateral A B C D , the point P divides D C in the ratio 1: 2 and Q is the mid point of A C . If A B +2 A D + B C -2 D C =k P Q , then k is equal to

Options

  1. A-6
  2. B-4
  3. C6
  4. D4

Correct answer

A. -6

Step-by-step solution

Now, A B +2 A D + B C -2 D C = A C +2 A D -2 D C = A C +2( A C + C D )-2 D C aligned & =3 A C -4 D C & =3(2 Q C )-4 ( 3 2 P C ) & =6 Q C -6 P C =6( Q C + C P ) aligned k P Q =6 Q P =-6 P Q (given) k=-6

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