Find the general form of the equation of the plane passing through the three points. [Be sure to reduce the coefficients in your answer to lowest terms by dividing out any common factor.]
$$( - 2 , - 1,4 ) , ( 3 , - 1,2 ) , ( - 6 , - 5 , - 6 )$$
A) $4 x - 29 y + 10 z - 61 = 0$
B) $4 x - 29 y + 10 z = 0$
C) $2 x + y - 4 z = 0$
D) $4 x - 29 y + 10 z + 61 = 0$
E) $2 x + y - 4 z + 122 = 0$

Question

Quizplus · Accepted Answer

To find the equation of the plane, we first find two vectors in the plane using the given points, then take their cross product to find the normal vector. Using the normal vector and one of the points, we can write the equation of the plane. After simplifying, the equation is $4x - 29y + 10z - 61 = 0$.

Find the General Form of the Equation of the Plane (−2,−1,4),(3,−1,2),(−6,−5,−6)( - 2 , - 1,4 ) , ( 3 , - 1,2 ) , ( - 6 , - 5 , - 6 )(−2,−1,4),(3,−1,2),(−6,−5,−6)

Find the General Form of the Equation of the Plane $( - 2 , - 1,4 ) , ( 3 , - 1,2 ) , ( - 6 , - 5 , - 6 )$