Question

Find the vector equation of the plane passing through the point A (4, - 2,3 ) and parallel to the plane x + 2 y - 5 z + 8 = 0

Answer 1

$A(4,-2,3)paralleltoplanex+2y-5z+8=0$

Normal vector to plane is $(1,2,-5)$

$(1,2,-5)(x-4,y+2,z-3)=0$

$(x-4)+2(y+2)-5(z-3)=0$

$x-4+2y+4-5z+3=0$

$x+2y-5z=-3$