JEE Main20252 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

If the image of the point P (1,0,3) in the line joining the points A (4,7,1) and B (3,5,3) is Q ( , , ) , then + + is equal to

Options

A47 3
B46 3
C18
D13

Correct answer

B. 46 3

Step-by-step solution

aligned & P (1,0,3) & A (4,7,1), B (3,5,3) & Line AB x -3 1 = y -5 2 = z -3 -2 = aligned Let foot of perpendicular of P on AB be aligned & R ( +3,2 +5,-2 +3) & ( +3-1)(1)+(2 +5-0)(2)+(-2 +3-3) & (-2)=0 & +2+4 +10+4 =0 & =- 4 3 & R ( 5 3 , 7 3 , 17 3 ) & Q ( 10 3 -1, 14 3 -0, 34 3 -3 ) ( 7 3 , 14 3 , 25 3 ) & + + = 7+14+25 3 = 46 3 aligned

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