1. Tardigrade
  2. Question
  3. Mathematics
  4. A plane containing the point (3, 2, 0) and the line (x-1/1)=(y-2/5)=(z-3/4) also contains the point :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A plane containing the point $(3, 2, 0) $ and the line $\frac{x-1}{1}=\frac{y-2}{5}=\frac{z-3}{4}$ also contains the point :

JEE MainJEE Main 2015Three Dimensional Geometry

Solution:

Equation of plane containing the point $A(3,2,0)$ and the line
$\begin{vmatrix}x-1 & y-2 & z-3 \\ 3-1 & 2-2 & 0-3 \\ 1 & 5 & 4\end{vmatrix}=0$
i.e., $(x-1)(15)-(y-2)(11)+(z-3)(10) =0$
i.e. $15 x-11 y+10 z-23=0$
clearly $(0,7,10)$ satisfy it, as
$15(0)-11(7)+10(10)-23 =-77+100-23=0$