Question

Find the reflection of the line x − 2y + 3z − 4 = 0 = 2x + 3y + 4z − 5 in the plane z = 0.​

Answer 1

Answer:

Using the fact that reflection of a

′

x+b

′

y+c

′

z+d

′

=0 in the plane ax+by+cz+d=0 is given by

2(aa

′

+bb

′

+cc

′

)(ax+by+cz+d)=(a

2

+b

2

+c

2

)(a

′

x+b

′

y+c

′

z+d

′

)

Given:2x−3y+4z=3 where a

′

=2,b

′

=−3,c

′

=4,d

′

=−3

x−y+z=3 where a=1,b=−1,c=1,d=−3

Required equation is 2(2+3+4)(x−y+z−3)=(1+1+1)(2x−3y+4z−3)

⇒6(x−y+z−3)=2x−3y+4z−3

⇒4x−3y+2z−15=0

Answer 2

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