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COMEDK2023Evening ShiftMathematicsThree Dimensional GeometryActual

P is a point on the line segment joining the points (3,2,-1) and (6,2,-2) . If the x co ordinate of P is 5 , then its y coordinate is

Options

  1. A-1
  2. B2
  3. C-2
  4. D1

Correct answer

B. 2

Step-by-step solution

Let the points be A(3, 2, -1) and B(6, 2, -2) . Let P(x, y, z) be a point on the line segment AB such that P divides AB in the ratio k:1 . Using the section formula, the coordinates of P are given by: x = k(6) + 1(3) k+1 , y = k(2) + 1(2) k+1 , z = k(-2) + 1(-1) k+1 Given that the x -coordinate of P is 5 , we have: 5 = 6k + 3 k+1 5(k+1) = 6k + 3 5k + 5 = 6k + 3 k = 2 Now, substitute k = 2 into the expression for the y -coordinate: y = 2(2) + 1(2) 2+1 = 4 + 2 3 = 6 3 = 2 Answer: 2

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