Find the general form of the equation of the plane passing through the three points. $( 0,0,0 ) , ( 5,6,7 ) , ( - 6,7,7 )$
A) $- 7 x + 71 y + 77 z = 0$
B) $- 7 x - 77 y - 71 z = 0$
C) $- 7 x - 77 y + 71 z = 0$
D) $- 7 x + 77 y - 71 z = 0$
E) $- 7 x + 77 y + 71 z = 0$

Question

Find the general form of the equation of the plane passing through the three points.  $( 0,0,0 ) , ( 5,6,7 ) , ( - 6,7,7 )$ 
A) $- 7 x + 71 y + 77 z = 0$
B) $- 7 x - 77 y - 71 z = 0$
C) $- 7 x - 77 y + 71 z = 0$
D) $- 7 x + 77 y - 71 z = 0$
E) $- 7 x + 77 y + 71 z = 0$

Quizplus · Accepted Answer

The equation of the plane passing through the three points can be found using the cross product of the vectors formed by the three points. The cross product of the vectors $( 5,6,7 ) - ( 0,0,0 )$ and $( - 6,7,7 ) - ( 0,0,0 )$ is $(- 7,77,71 )$. This vector is normal to the plane, so the equation of the plane is $- 7 x + 77 y + 71 z = 0$.

Find the General Form of the Equation of the Plane (0,0,0),(5,6,7),(−6,7,7)( 0,0,0 ) , ( 5,6,7 ) , ( - 6,7,7 )(0,0,0),(5,6,7),(−6,7,7)

Find the General Form of the Equation of the Plane $( 0,0,0 ) , ( 5,6,7 ) , ( - 6,7,7 )$