Answer to Question #216859 in Analytic Geometry for Buzz

Question

Find the vector form of the equation of the plane passing through the point P (1-23) and has normal vector n <3,1, - 1>

Answer 1

Solution:

Given, point P(1,-2,3), Normal vector = <3,1,-1>

$\overrightarrow a=(x_0,y_0,z_0)=(1,-2,3),\overrightarrow N=<A,B,C>=<3,1,-1>$

Vector equation: $(\overrightarrow r-\overrightarrow a).\overrightarrow N=0$

$\Rightarrow (\overrightarrow r-(\hat i-2\hat j+3\hat k)).(3\hat i+\hat j-\hat k)=0$

$\Rightarrow (\overrightarrow r-\hat i+2\hat j-3\hat k).(3\hat i+\hat j-\hat k)=0$