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Question:

The plane containing the line x-3/2 = y+2/1 = z/3 and also containing its projection on the plane 2x+3y-z=5, contains which one of the following point?

(2,0,-6)

(-6,2,2)

(0,-6,2)

(2,2,0)

Solution:

The correct option is A(2,0,-6)
The normal vector of required plane=(2i-j+3k) x (2i+3j-k) = -8i+8j+8k
So, direction ratio of normal is(-8,8,8)
So required plane is -(x-3)+(y+2)+(z-0)=0
-x+3+y+2+z=0
-x+y+z+5=0
-x+y+z=-5
Which is satisfied by (2,0,-6)