1103189001

Find the general form of the equation of the plane $\alpha$ that is perpendicular to the straight line $p$ given by: $$\begin{array}{rl}x& =7+t,\\ y& =2t,\\ z& =4-t;t\in \mathbb{R},\end{array}$$ and passes through the point $A=[1;0;4]$. Consequently, find the coordinates of the point $B$ which is the point of intersection of $p$ and $\alpha$ (see the picture).