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AP EAMCET20224 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

If 2 , 3 , c are the direction ratios of a ray passing through the point C 5 , q , 1 and also the mid point of the line segment joining the points A p , - 4 . 2 and B 3 , 2 , - 4 then c . p + 7 q =

Options

  1. A17
  2. B34
  3. C21
  4. D28

Correct answer

B. 34

Step-by-step solution

The mid point of the line segment joining the points A p , - 4 . 2 and B 3 , 2 , - 4 is given by M p + 3 2 , - 1 , - 1 Now given 2 , 3 , c is direction ratio of line which passing through C 5 , q , 1   &   M p + 3 2 , - 1 , - 1 So, by direction ratio formula between two points we get, p + 3 2 - 5 = 2 ⇒ p = 11 - 1 - q = 3 ⇒ q = - 4 - 1 - 1 = c ⇒ c = - 2 Now solving c . p + 7 q by using above value we get, c . p + 7 q = - 2 × 11 - 28 = 34

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