Question

Find the Cartesian equation of the plane passing through A(1, 2, 3) and the  direction ratios of whose normal are 3, 2, 5​

Answer 1

$\textbf{Given:}$

$\textsf{The plane passes through (1,2,3) and direction ratios of normal are 3,2,5}$

$\textbf{To find:}$

$\textsf{The cartesian equation of the plane}$

$\textbf{Solution:}$

$\textsf{The equation of the plane passes through}\;\mathsf{(x_1,y_1,z_1)}$

$\textsf{and direction ratios of normal are (a,b,c) is given by}$

$\mathsf{a(x-x_1)+b(y-y_1)+c(z-z_1)=0}$

$\implies\mathsf{3(x-1)+2(y-2)+5(z-3)=0}$

$\implies\mathsf{3x-3+2y-4+5z-15=0}$

$\implies\boxed{\mathsf{3x+2y+5z-22=0}}$

$\textbf{Answer:}$

$\textsf{Equation of the required plane is 3x+2y+5z-22=0}$

$\textbf{Find more:}$

find the equation of the plane passing through the point (3, -2, 1) and perpendicular to the vector (4, 7, -4)

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