How to Deduce the Normal Vector from a Given Vector Equation?

[acpower89]

I'm having trouble finding the equation normal to the plane for part (ii).

The vector equation I got for part (i) is r=(1/2,1,2/3) + t(3/2,2,-2/3). How do you deduce the normal vector from this? The answer is the vector (9,12,-4). I've tried anything but don't know where they got this result.

Thanks

 

[algebrat]

They used your (3/2,2,-2/3) and multiplied by 6 to clear the denominator.