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MHT CET202416 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The length 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 units
  2. B2 3 units
  3. C2 3 units
  4. D2 3 units

Correct answer

A. 2 3 units

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 | & aligned = 2 6 = 1- 4 6 = 1 3 aligned & Required projection =| AB | & = 2 1 3 = 2 3 units aligned

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