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line = ParametricPlot3D[{0, t, 0}, {t, -1, 1}, PlotStyle -> {Red, Thick}, Boxed -> False, Axes -> None];
pt = Graphics3D[{PointSize[0.04], Point[{0, 0, 0}]}, Boxed -> False];
Show[line, pt, ImageSize -> 600]

enter image description here

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2 Answers 2

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Is this what you want?

enter image description here

line = ParametricPlot3D[{0, t, 0}, {t, -1, 1}, 
   PlotStyle -> {Red, Thick}, Boxed -> False, Axes -> None];
pt = Graphics3D[{PointSize[0.04], Point[{0, 0, 0}]}, Boxed -> False];
Overlay[{line, pt}, ImageSize -> 300]
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Using Ball instead of Point, avoiding using Show and using "3DRenderingMethod" -> "BSPTree" depicts the 3D scene correctly under different viewpoints.

line = ParametricPlot3D[{0, t, 0}, {t, -1, 1}, 
   PlotStyle -> {Red, Thick}, Boxed -> False, Axes -> None];

point = {Black, Ball[{0, 0, 0}, {0.1}]};

Style[Replace[line, 
  Graphics3D[x_, y___] :> Graphics3D[Append[x, point], y], All], 
 RenderingOptions -> {"3DRenderingMethod" -> "BSPTree"}]

enter image description here

enter image description here

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