The image of the point A(1,2,3) relative to the plane π is B(3,6,−1). The equation of the plane π is
A
x+2y+3z−1=0
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B
x+2y−2z+8=0
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C
x−2y+2z−8=0
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D
x+2y−2z−8=0
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Solution
The correct option is Dx+2y−2z−8=0 Midpoint of segment AB is (1+32,2+62,3−12)≡(2,4,1) Direction ratios of segment (normal) AB are (2,4,−4) Hence, equation of the plane π is given by 2(x−2)+4(y−4)−4(z−1)=0 ⇒2x+4y−4x−16=0 ⇒x+2y−2z−8=0