Find the vector equation of the line passing through the point (1,2,3) and parallel to the planes ` vec rdot( hat i- hat j+2 hat k)=5` and ` vec rdot(3 hat i+ hat j+ hat k)=6.`

Explanation

`P_1=vecr*(hati-hatj+2hatk)=5`

`vecn_1=hati-hatj+2hatk`

`P_2=vecr*(3hati+hatj+hatk)=6`

`vecn=3hati+hatj+hatk`

`l=vecr=veca+lambdavecb`

`vecb=vecn_1*vecn_2`

`=i(-1-2)-j(1-6)+k(1-(-3))`

`vecb=-3hati+5hatj+4hatk`

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