Question

Find the equation of a plane that is perpendicular to the vector −4i⃗ −4j⃗ −k⃗ and passing through the point (−2,−5,5)

Answer 1

hello ....

the equation of a plane that is ;  ax+by+cz +d =0

the vector perpendicular to this plane is : V(a,b,c)

in this exercice ; a = -4  b= -4  c = -1

then: the equation of a plane that is ;  -4x-4y-z +d =0

but the plane  passing through the point (−2,−5,5) :

-4(-2)-4(-5)-(5) +d =0

23+d =0

d =-23

the equation of a plane is : -4x-4y-z-23 =0