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

AM ⋅ ( 2 i ^ + 3 j ^ + 5 k ^ ) = 0 ( 2 λ − 7 ) ( 2 ) + ( 3 λ − 6 ) ( 3 ) + ( 5 λ − 5 ) ( 5 ) = 0 38 λ = 57 λ = 2 3 M ( 4 , 2 7 , 2 19 ) A ′ ( 0 , 2 , 12 )

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MathematicsVectorVector equation of a line, Vector equation of the angle bisectorsEasy2 minPYQ_2024

MathematicsEasysingle choice

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 :

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Answer:

Solution:

$AM \cdot (2 \hat{i} + 3 \hat{j} + 5 \hat{k}) = 0 (2 λ - 7) (2) + (3 λ - 6) (3) + (5 λ - 5) (5) = 0 38 λ = 57 λ = \frac{3}{2} M (4, \frac{7}{2}, \frac{19}{2}) A^{'} (0, 2, 12)$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Vector equation of a line, Vector equation of the angle bisectors

⏱ 2mℹ️ Source: PYQ_2024

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