Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryPlane (Equations)Medium2 minPYQ_2016

MathematicsMediumsingle choice

If $A$ and $B$ are foot of perpendicular drawn from point $Q (a, b, c)$ to the planes $y z$ and $z x$ , then equation of plane through the points $A, B$ and $O$ is _______

Options:

Answer:

Solution:

$A (0, b, c)$
$B (a, 0, c)$
Equation of plane is $|\begin{matrix} x & y & z & 1 \\ 0 & b & c & 1 \\ a & 0 & c & 1 \\ 0 & 0 & 0 & 1 \end{matrix}| = 0$
$\Rightarrow |\begin{matrix} x & y & z \\ 0 & b & c \\ a & 0 & c \end{matrix}| = 0$
$\Rightarrow b c x + c a y - a b z = 0$
$\Rightarrow \frac{x}{a} + \frac{y}{b} - \frac{z}{c} = 0$

Stream:MHT_CETSubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Plane (Equations)

⏱ 2mℹ️ Source: PYQ_2016

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