QJEEM24Ma3cb0: JEE Main 2024 Mathematics - Class 12 JEEM24Ma3cb0 Solution: Let ( α , β , γ ) be the image of the point ( 8 , 5 , 7 ) in…

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QJEEM24Ma3cb0: JEE Main 2024 Mathematics - Class 12 JEEM24Ma3cb0 Solution: Let ( α , β , γ ) be the image of the point ( 8 , 5 , 7 ) in…

Let $(α, β, γ)$ be the image of the point $(8, 5, 7)$ in the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 2}{5}$ . Then $α + β + γ$ is equal to :

Multiple Choice Options

A 16
B 20
C 18
D 14

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Accepted Answer

$(x, y, z) \equiv (2 λ + 1, 3 λ + 1, 5 λ + 2)$

JEE Main 2024 (Online) 5th April Evening Shift Mathematics - 3D Geometry Question 23 English Explanation

DR of $P Q$ :

$(2 λ - 7, 3 λ - 6, 5 λ - 5)$

DR of line : $(2, 3, 5)$

$\begin{array}{ll} ∴ & 2 (2 λ - 7) + 3 (3 λ - 6) + 5 (5 λ - 5) = 0 \\ \Rightarrow & λ = \frac{3}{2} \\ ∴ & Q (4, \frac{7}{2}, \frac{19}{2}) \\ ∴ & (α, β, y) \equiv (0, 2, 12) (Q is mid point of P & P^{'}) \\ α + β + y \equiv 14 \end{array}$

QJEEM24Ma3cb0: JEE Main 2024 Mathematics - Class 12 JEEM24Ma3cb0 Solution: Let ( α , β , γ ) be the image of the point ( 8 , 5 , 7 ) in…

Multiple Choice Options

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