Question

Find the vector equation of the plane which is normal to the vector $\hat{i}+\hat{j}+\hat{k}$ and passes through the point $(2,3,4)$. Also, find its cartesian equation.

Answer 1

Given normal vector is..

$=i+j+k$ ,passes through the point, (2,3,4)

suppose,

$n=(x-x_1,y-y_{1}z-z_1)=0$

then,

$\Rightarrow (1,1,1)(x-2,y-3,z-4)=0$

$\Rightarrow 1(x-2)+1(y-3)+1(z-4)=0$

$\Rightarrow x-2+y-3+z-4=0$

so that, cartesian equation is

$\therefore x+y+z=9$