What is the equation of the plane passing through `(x_1,y_1,z_1)` and normal to the line with lt a, b, c gt as firection ratios ?

Options

A. `ax+by+cz=ax_1+by_1+cz_1`
B. `a(x+x_1)+b(y+y_1)+c(z+z_1)=0`
C. `ax+by+cz=0`
D. `ax+by+cz=x_1+y_1+z_1=0`

Answer

A

Explanation

The equation of the plane passing through `(x_1,y_1,z_1)` and normal to the line with lt a, b, cgt as direction ratios, is given by :
`a(x-x_1)+b(y-y_1)+c(z-z_1)=0`
`rArrax-ax_1+by-by_1+cz-cz_1=0`
`rArr ax+by+cz=ax_1+by_1+cz_1`
Which is required equation of plane.