Reflection of the line x-1/-1 = y-2/3 = z-4/1 in the plane x+y+z=7 is

Correct Answer is : x−1−3=y−21=z−4−1x-1/-3 = y-2/1 = z-4/-1−3x−1=1y−2=−1z−4

Correct Answer is : x−1−3=y−21=z−4−1x-1/-3 = y-2/1 = z-4/-1−3x−1=1y−2=−1z−4

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BITSAT 2019 Slot 2 Solved Paper

Section: Mathematics

Question : 149 of 150

Marks: +1, -0

Reflection of the line

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

x+y+z=7

Solution:

Given line

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

is passes through

P(1,2,4)

To find the reflection of line we need one more point on the line clearly

M(0,5,5)

also lie on line. Let

N(\alpha, \beta, \gamma)

be the reflection

M

in the

x+y+z=7

\therefore \frac{\alpha}{2} + \frac{\beta+5}{2} + \frac{\gamma+5}{2} + 7

\Rightarrow

\alpha + \beta + \gamma = 4

Also,

M N

is perpendicular, i.e. parallel to the normal of the plane

\therefore \frac{\alpha}{1} = \frac{\beta-5}{1} = \frac{\gamma-5}{1} = \lambda

\Rightarrow \alpha = \lambda, \beta = \lambda + 5, \gamma = \lambda - 5

\therefore \lambda + \lambda + 5 + \lambda + 5 = 4

\Rightarrow \lambda = -2

\therefore N = (-2, 3, 5)

Equation

P N

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

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