Find the vector equation of a plane passing through intersectio of two planes
`vecr cdot (3hati +4hatj + 5hatk)=9 and vecr cdot (2hati - 3hatj +4hatk)=6` and which also passes through the point
(-1, 0, 1).

Explanation

We know that equation of plane passing through `vecr cdot vecn_(1)=d_(1) and vecr cdot vecn_(2)=d_(2)` is given by
`vecr cdot (vecn_(1)+lambda vecn_(2))=d_(1)+lambda d_(2)`
substituting given values
`vecr cdot ((3+2lambda )hati + (4-3lambda )hatj + (5+4lambda )hatk)=9 +6lambda`
This plane passes through (-1, 0, 1) so
`(-hati+hatk) cdot [(3+2lambda )hati + (4-3lambda )hatj + (5+4lambda )hatk]=9 +6lambda`
`-(3+2lambda ) + 5+ 4lambda =9+ 6lambda `
`2 +2lambda = 9 + 6lambda`
`4lambda = -7 rArr lambda =-7/4`
`vecr cdot [-1/2hati+37/4hatj-2hatk]=-3/2`
`vecr cdot [-2hati+37hatj-4hatk]=-6`