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AP EAMCET202021 Sep 2020Morning ShiftMathematicsVector AlgebraActual

Let ( u = i -2 j ) and ( v =-3 i +5 j ). Consider three points (P, Q ) and (R ) having position vectors ( -1 7 i , -1 4 j ) and (-2 i +3 j ) respectively. Among these, the points in the line segment passing through ( u ) and ( v ) are

Options

  1. AOnly (P ) and (Q )
  2. BOnly (P ) and (R )
  3. COnly (Q ) and (R )
  4. DAll (P, Q ) and (R )

Correct answer

A. Only (P ) and (Q )

Step-by-step solution

Given vectors ( u = i -2 j ) and ( v =-3 i +5 j ). Now, equation of line segment passes through the points ( u ) and ( v ) is ( x-1 4 = y+2 -7 ) ...(i) Now, the point vectors having position vectors ( O P =- 1 7 i , O Q =- 1 4 j ) and ( O R =-2 i +3 j ) are given. The point (P (- 1 7 , 0 ) ) by putting in line (i) ( - 1 7 -1 4 = 2 -7 -8 4 7 = 2 -7 -2 7 = 2 -7 ) ( ) Point (P (- 1 7 , 0 ) ) satisfied the line, so it is on the line segment (i) The point (Q (0,- 1 4 ) ) by putting in line (i) ( 0-1 4 = - 1 4 +2 7 - 1 4

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