A variable plane passes through a fixed point (3, 2, 1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz-plane through A, a second plane is drawn parallel zx-plane through B and a third plane is drawn parallel to xy-plane through C. Then the locus of the point of intersection of these three planes, is :
As we learned
Intercept form -
- wherein
Let the plane cuts the coordinate axis at
Let a,b,c be intercepts of plane on axis.
Equation of plane is
And point of intersection of plane is (a,b,c)
since (3,2,1) lies on variable plane
Locus will be
Option 1)
Option 2)
Option 3)
Option 4)
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