Answered

IDNStudy.com, kung saan ang iyong mga tanong ay may malinaw na sagot. Alamin ang mga detalyadong sagot mula sa mga bihasang miyembro ng aming komunidad na sumasaklaw sa iba't ibang paksa para sa lahat ng iyong pangangailangan.

Write an equation for the plane that contains the points (4,0,-6), (-8,-10,4), and (0,6,-8) in the form ax+by+cz=d

Sagot :

AnneCidn
To find the equation of the plane, we need to find its normal vector. To do this, we will get the cross product of two vectors on the plane.

There are many possible vectors, but let's use:
v1 = <12, 10, -10> 
v2 = <-8, -16, 12>  
v1 x v2 = <-40, -64, -112>   This is a normal vector of the plane.

Plugging these in to the equation in the point normal form, we have
-40(x-4) -64(y-0) -112(z+6) = 0

Simplify: -40x -64y -112z = 512   –––>    -5x -8y -14z = 64