Originally Posted by

**adkinsjr** I need to find the plane $\displaystyle A$ that contains the line $\displaystyle r_A(t)=<3+2t , t , 8-t>$ and is parallel to the plane $\displaystyle B, 2x+4y+8z=17$

I know that the normal vectors $\displaystyle n_A=<a,b,c>,n_B=<2,4,8>$ should have a dot product equal to one. also know that the points $\displaystyle (3,1,7),(7,2,6)$ lie on the line $\displaystyle r_A(t)$, correpsonding to $\displaystyle t=1,t=2$. The points are also the terminal points of the vectors $\displaystyle <3,1,7>,<7,2,6>$. Substracting these vectors, I write the vector equation of the plane $\displaystyle A$ as