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AP EAMCET202318 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

If a point R (4, y , z ) lies on the line joining the points P(2,-3,4) and Q(8,0,10) , then distance of R from origin is

Options

  1. A2 14
  2. B6
  3. C53
  4. D2 21

Correct answer

A. 2 14

Step-by-step solution

Equation of line joining point P and Q : x^ -2 8-2 = y^ +3 0+3 = z^ -4 10-4 = ( say ) x^ =6 +2, y^ =3 -3, z^ =6 +4 Point R (4, y , z ) lies on line PQ 4=6 +2 = 1 3 aligned & and y=3 -3=3 1 3 -3=-2 & z=6 +4=2+4=6 aligned Point R (4,-2,6) Now, distance of R from origin is = 16+4+36 = 56 =2 14

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