The equation of plane which passes through the point of intersection of lines
`vecr=hati+2hatj+3hatk+lamda(3hati+hatj+2hatk)` and `vecr=3hati+hatj+2hatk+mu(hati+2hatj+3hatk)` where `lamda,muinR` and has the greastest distance from the origin is :

Options

A. `vecr.(7hati+2hatj+4hatk)=54`
B. `vecr.(5hati+4hatj+3hatk)=57`
C. `vecr.(3hati+4hatj+5hatk)=49`
D. `vecr.(4hati+3hatj+5hatk)=50`

Answer

D

Explanation

For point of intersection
`1+3lamda=3+mu`
`2+lamda=1+2mu`
`5lamda=5implieslamda=1,mu=1`
Point of intersection (4,3,5)
For greatest distance from origin perpendicular from meet plane at point of intersection
Hence equation `vecr.(4hati+3hatj+5hatk)=50`