Let P be the image of the point (3, 1, 7) with respect to the plane x - y + z = 3. Then, the equation of the plane passing through P and containing the straight line x1=y2=z1 is
x - 4y + 7z = 0
Let image of Q(3,1,7) w.r.t. x - y + z = 3 be P(α,β,γ).∴ α−31=β−1−1=γ−71=−2(3−1+7−)12+(−1)2+(1)2⇒α−3=1−β=γ−7=−4∴ α=−1,β=5,γ=3
Hence, the image of Q(3, 1, 7) is P(-1, 5, 3).
To find equation of plane passing through P(-1, 5, 3) and containing x1=y2=z1
⇒ ∣∣
∣∣x−0 y−0 z−01−0 2−0 1−0−1−0 5−0 3−0∣∣
∣∣=0⇒x(6−5)−y(3+1)+z(5+2)=0x−4y+7z=0