Find-the-image-of-the-line-x-2-1-y-3-2-z-4-3-in-the-plane-2x-3y-4z-3-0-

Question Number 75317 by vishalbhardwaj last updated on 10/Dec/19

Find the image of the line

\frac{x - 2}{- 1} = \frac{y - 3}{2} = \frac{z - 4}{3} in the plane

2 x + 3 y - 4 z + 3 = 0 .

Commented by vishalbhardwaj last updated on 10/Dec/19

yes sir, I corrected it

Answered by vishalbhardwaj last updated on 10/Dec/19

please solve this

Answered by mr W last updated on 10/Dec/19

l i n e

\frac{x - 2}{- 1} = \frac{y - 3}{2} = \frac{z - 4}{3} = λ

\Rightarrow x = - λ + 2

\Rightarrow y = 2 λ + 3

\Rightarrow z = 3 λ + 4

u s i n g λ = 1 w e g e t a p o i n t P o n t h e

l i n e P (1, 5, 7) .

s a y t h e i m a g e o f p o i n t P i n t h e

p l a n e i s P^{'} (u, v, w)

(x, y, z) = (1, 5, 7) + k (2, 3, - 4)

2 (1 + 2 k) + 3 (5 + 3 k) - 4 (7 - 4 k) + 3 = 0

\Rightarrow k = \frac{8}{3}

(u, v, w) = (1, 5, 7) + \frac{16}{3} (2, 3, - 4) = (\frac{35}{3}, 21, \frac{- 43}{3})

i n t e r s e c t i o n p o i n t Q o f l i n e a n d p l a n e :

2 (- λ + 2) + 3 (2 λ + 3) - 4 (3 λ + 4) + 3 = 0

\Rightarrow λ = 0

\Rightarrow Q (2, 3, 4)

t h e i m a g e o f l i n e i n p l a n e i s t h e

l i n e P^{'} Q :

\frac{x - 2}{\frac{35}{3} - 2} = \frac{y - 3}{21 - 3} = \frac{z - 4}{- \frac{43}{3} - 4}

\Rightarrow \frac{x - 2}{\frac{29}{3}} = \frac{y - 3}{18} = \frac{z - 4}{- \frac{55}{3}}

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