Answer to Question #245705 in Analytic Geometry for luka

Question

Write down the equation of the plane containing the point (2 , 3 , 4 ) and parallel to

the vectors

u= (2 , -3 ,2) and v= (0 , 1 , 2) .

Answer 1

$$u\times v=\begin{vmatrix} i & j & k \\ 2 & -3 & 2 \\ 0 & 1 & 2 \\ \end{vmatrix}$$

$$=i\begin{vmatrix} -3 & 2 \\ 1 & 2 \end{vmatrix}-j\begin{vmatrix} 2 & 2 \\ 0 & 2 \end{vmatrix}+k\begin{vmatrix} 2 & -3 \\ 0 & 1 \end{vmatrix}$$

$$=-8i-4j+2k$$

$$n=(-8,-4,2)$$

The equation of the plane containing the point (2 , 3 , 4 )

$$-8(x-2)-4(y-3)+2(z-4)=0$$

$$4(x-2)+2(y-3)-(z-4)=0$$

$$4x-8+2y-6-z+4=0$$

$$4x+2y-z-10=0$$