Show-that-following-points-are-coplanar-ii-0-4-3-1-5-3-2-2-1-1-1-1 - Mathematics

प्रश्न

Show that the following points are coplanar.

(0, 4, 3), (−1, −5, −3), (−2, −2, 1) and (1, 1, −1)

योग

उत्तर

(ii) The equation of the plane passing through (0, 4, 3), (−1, −5, −3), (−2, −2, 1) is

$| \begin{matrix} x - 0 & y - 4 & z - 3 \\ - 1 - 0 & - 5 - 4 & - 3 - 3 \\ - 2 - 0 & - 2 - 4 & 1 - 3 \end{matrix} | = 0$
$\Rightarrow | \begin{matrix} x & y - 4 & z - 3 \\ - 1 & - 9 & - 6 \\ - 2 & - 6 & - 2 \end{matrix} | = 0$
$\Rightarrow - 18 x + 10 (y - 4) - 12 (z - 3) = 0$
$\Rightarrow 9 x - 5 (y - 4) + 6 (z - 3) = 0$
$\Rightarrow 9 x - 5 y + 6 z + 2 = 0$
$Substituting the last point (1, 1, -1) (it means x = 1; y = 1; z=-1) in this plane equation, we get$
$9 (1) - 5 (1) + 6 (- 1) + 2 = 0$
$\Rightarrow 4 - 4 = 0$
$\Rightarrow 0 = 0$
$So, the plane equation is satisfied by the point (1, 1, -1) .$
$So, the given points are coplanar .$

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Equation of a Plane - Equation of a Plane Passing Through Three Non Collinear Points

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 3.2 Q 3.1 Q 4

अध्याय 29: The Plane - Exercise 29.01 [पृष्ठ ५]

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अध्याय 29 The Plane
Exercise 29.01 | Q 3.2 | पृष्ठ ५

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