a given point (a) Vector form of equation Consider a plane passing through a point A with position vector a and n is a normal vector to the given plane. Let r be the position vector of an arbitrary point P on the plane. Fig. .
Fig. . r ˆ d pd P O P Vector - - Applications of Vector Algebra Then AP is perpendicular to n . So, AP n which gives ( ...
( ) which is the vector form of the equation of a plane passing through a point with position vector a and perpendicular to n . Note = ⇒ r n a n ⋅ ⇒ r n q , where q a n . (b) Cartesian form of equation If , , a b c are the direction ratios of n , then we have ai bj ck . Suppose, A is ( , x y z then equation ( ) becomes ˆ (( ) ) ( x i z k ai bj ck .
That is, a x b y c z = which is the Cartesian equation of a plane, normal to a vector with direction ratios , , a b c and passing through a given point ( , x y z