Question

how can we find a normal vector from the equ of aplane give reasons of ur ans

Answer 1

rearrange the eqn of a plane in the form ax +by + cz +d=0
the normal vector is <a,b,c>

Answer 2

give reasons why we do this

Answer 3

suppose any known vector k, and normal vector n
then the eqn of the plane is (r-k).n = 0
if you expand this, youll see the coefficients of x, y, z in cartesian form are the direction ratios of the normal vector

Answer 4

PS : k is the position vector of a known pt on the plane

Answer 5

what are direction ratios??

Answer 6

consider a plane equation in its primary form (r-k).n=0 (where n->normal vector & k-> is the position vector of the plane) and when u expand this using simple dot product then finally u will get that coefficients of x,y,z gives u the dierection ratios
direction ratios are the ratio of the magnitude of vector in one direction to the magnitude in the resultant direction.