Define angle between "3D space" in 4D space

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We can define the angle between the line in 2D space, and also can define angle between planes in 3D space, and is it possible to define the angle between 3D space in higher dimensions? And if it's possible to define, and can I use this formula, $V=V^\prime \cos\theta$ to get a volume of "orthogonal projection" of the solid?