How to find the normal to the plane r = (3,-6,8) + t(4,2,1) + s(-4,3,-2)?

　
Take cross product of the two vectors parallel to plane:
< 4, 2, 1 > × < −4, 2, −2 > = < −6, 4, 16 >

So normal can be any vector parallel to < −6, 4, 16 >

N = < 3, −2, −8 >