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Question

Let P be the image of the point (3,1,7) with respect to the plane xy+z=3. Then the equation of the plane passing through P and containing the straight line x1=y2=z1 is

A
x+y3z=0
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B
3x+z=0
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C
x4y+7z=0
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D
2xy=0
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Solution

The correct option is C x4y+7z=0

Let image of point (3,1,7) with respect to the plane xy+z=3 is P(h,k,l)
h31=k11=l71=2(31+73)3=4
After solving, we get
h=1,k=5,l=3
Therefore, the image is P(1,5,3)

Also, required plane contains the straight line x1=y2=z1
The plane passes through (0,0,0) and (1,2,1)
Therefore, required equation of the plane passing through the three points is
∣ ∣ ∣x0y0z00102010(1)0503∣ ∣ ∣=0

x4y+7z=0

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