3D Geometry 3 Question 35

####35. 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

(2016 Adv.)

(a) x+y3z=0

(b) 3x+z=0

(c) x4y+7z=0

(d) 2xy=0

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Answer:

Correct Answer: 35. (c)

Solution:

  1. Let image of Q(3,1,7) w.r.t. xy+z=3 be P(α,β,γ).

α31=β11=γ71=2(31+73)12+(1)2+(1)2α3=1β=γ7=4α=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

|x0y0z0102010105030|=0

x(65)y(3+1)+z(5+2)=0x4y+7z=0



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