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MHT CET202312 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The length (in units) of the projection of the line segment, joining the points (5,-1,4) and (4,-1,3) , on the plane x+y+z=7 is

Options

  1. A2 3
  2. B2 3
  3. C2 3
  4. D2 3

Correct answer

D. 2 3

Step-by-step solution

aligned & Let A=(5,-1,4), B=(4,-1,3) & AB =- i - k | AB |= 2 aligned Projection of AB in the plane x+y+z=7 is | AB | = | A ^ B ^ | Direction ratios of normal to the given plane is 1,1,1 . aligned & (90^ - )= | 1(-1)+1(0)+1(-1) 1^2+1^2+1^2 1^2+0^2+1^2 | & array r = 2 6 = 1- 4 6 = 1 3 Required projection =| AB | = 2 1 3 = 2 3 array aligned

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