Answer:
21x-24y-15z=36
Step-by-step explanation:
The equation of a plane is given a s
ax+by+cz=d
where a,b,c and d are gotten from the vector product of the vector define by subtracting one of the given points from the other two
Hence we define the vectors as follow
<3,-2,5> - <-3,-1,-5> = <6,-1,10>
also <0,-4,4> - <-3,-1,-5>=<3,-3,9>
Next we need to carry out the cross product of the newly formed vector
<6,-1,10> X <3,-3,9> =<21,-24,-15>
The newly formed vector is in orthogonal to both vector and in direction to the normal vector to the plane.
Since ax+by+cz=d is the normal vector, we can conclude that
a=21, b=-24 c=-15
Hence we have
21x-24y-15z=d
if we plug in the point <-3,-1,-5> to solve for "d" we arrive at
21(-3)-24(-1)-15(-5)=36
Hence the final equation is
21x-24y-15z=36
