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Introduction To 3D Coordinate Geometry — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsIntroduction To 3D Coordinate Geometry1 Mark
Question
Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at $(3, -5, 7)$ and $(3, 0, 1)$.
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Answer

Let the coordinates of third vertex be $(x_1, y_1, z_1)$
Now,
$\frac{\text{x}_1+3+3}{3}=0,\ \frac{\text{y}_1+5+0}{3}=0\text{ and }\frac{\text{z}_1+7+1}{3}=0$
$\Rightarrow\text{x}_1 = −6,\ \text{y}_1 = 5\text{ and }\text{z}_1 = −8$
Hence, the coordinates of third vertex of a triangle is $(−6, 5, −8)$.

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