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JEE Main202228 Jun 2022Evening ShiftMathematicsThree Dimensional GeometryActual

Let the image of the point P 1 , 2 , 3 in the line L : x - 6 3 = y - 1 2 = z - 2 3 be Q . let R α , β , γ be a point that divides internally the line segment P Q in the ratio 1 : 3 . Then the value of 22 α + β + γ is equal to

Correct answer

0

Step-by-step solution

Plotting the rough graph of the given data we have, Let M be the mid-point of P Q ∴   M = 3 λ + 6 , 2 λ + 1 , 3 λ + 2 Now, P M → = 3 λ + 5 i ^ + 2 λ - 1 j ^ + 3 λ - 1 k ^ ∵   P M → ⊥ 3 i ^ + 2 j ^ + 3 k ^ ∴   3 3 λ + 5 + 2 2 λ - 1 + 3 3 λ - 1 = 0 λ = - 5 11 ∴   M 51 11 , 1 11 , 7 11 Since R is mid-point of P M So by using midpoint formula in P   &   M we get, R = 62 22 , 23 22 , 40 22 , now

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