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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 83

Equation of the plane which passes through the point of intersection of lines
x−13=y−21=z−32andx−31=y−12=z−23\frac{x-1}3=\frac{y-2}1=\frac{z-3}2\quad\text{and}\quad\frac{x-3}1=\frac{y-1}2=\frac{z-2}3
and has the largest distance from the origin is :

Choose one option
Answer and worked solution

Official answer: C

Intersection. Equate (1+3t,2+t,3+2t)=(3+s,1+2s,2+3s)(1+3t,2+t,3+2t)=(3+s,1+2s,2+3s): s=t=1s=t=1, giving P(4,3,5)P(4,3,5).

Plane. Among planes through PP, the one farthest from the origin is perpendicular to OPOP:
4x+3y+5z=50.4x+3y+5z=50.

Topics:Equation of a planeEquation of a line in space
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