Question

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

Answer 1

$\textbf{To find:}$

$\textsf{The equation of the plane passing through (3,-2,1) and}$

$\textsf{perpendicular to the vector (4,7,-4)}$

$\textbf{Solution:}$

$\textsf{Formula used:}$

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

$\mathsf{perpendicuar\;to\;(a,b,c)\;is}$

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

$\textsf{The required plane is}$

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

$\mathsf{4(x-3)+7(y+2)-4(z-1)=0}$

$\mathsf{4x-12+7y+14-4z+4=0}$

$\boxed{\mathsf{4x+7y-4z+6=0}}$

$\textbf{Find more:}$

Find vector equation of plane which passes through the points (3,2,1) and (0,1,7) and is parallel to line r=2i-j+k+l(i-j-k)

https://brainly.in/question/8252354

Answer 2

$\textbf{To find:}$

$\textsf{The equation of the plane passing through (3,-2,1) and}$

$\textsf{perpendicular to the vector (4,7,-4)}$

$\textbf{Solution:}$

$\textsf{Formula used:}$

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

$\mathsf{perpendicuar\;to\;(a,b,c)\;is}$

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

$\textsf{The required plane is}$

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

$\mathsf{4(x-3)+7(y+2)-4(z-1)=0}$

$\mathsf{4x-12+7y+14-4z+4=0}$

$\boxed{\mathsf{4x+7y-4z+6=0}}$