Find both the vector equation and the parametric equations of the line through (0,0,0) that is perpendicular to both uequalsleft angle 2 comma 0 comma 2 right angle and wequalsleft angle negative 2 comma 1 comma 0 right angle where tequals0 corresponds to the given point.

The equation of the line and its parametric equations are and .

Vectorially speaking, the equation of the line is defined by the following formula:

(1)

Where:

Since must be perpendicular both to and , then we must apply cross product:

(2)

Then, we have the following equation of the line: (,  )

 (3)

And the parametric equations are, respectively:

(4)

The equation of the line and its parametric equations are and .

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Find both vector equation and the parametric equations of the line through (0, 0, 0) that is perpendicular to the following two vectors: , .

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