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kathialopez
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Determine vector and parametric equations for the z-axis.
HOW DO YOU ANSWER THIS QUESTION?
HOW DO YOU ANSWER THIS QUESTION?
kathialopez said:Determine vector and parametric equations for the z-axis.
HOW DO YOU ANSWER THIS QUESTION?
A vector equation for the z-axis can be written as r = ti + tj + zk, where r is the position vector, t is a scalar parameter, and i, j, and k are unit vectors in the x, y, and z directions respectively.
The parametric equations for the z-axis can be determined by setting the x and y components of the vector equation equal to zero. This results in the equations x = 0 and y = 0. The z component of the vector equation, z = tk, becomes the parametric equation for the z-axis.
No, the equations for the z-axis do not represent a specific point but rather a line passing through the origin in the z direction. To represent a point on the z-axis, the scalar parameter t must be given a specific value.
To graph the z-axis, plot points by assigning different values to the scalar parameter t in the parametric equation. This will result in a line passing through the origin and extending infinitely in the z direction. Alternatively, the vector equation can be graphed by plotting the x, y, and z coordinates of the points on a three-dimensional coordinate system.
Yes, the vector and parametric equations for the z-axis are unique and cannot be interchanged with equations for other axes. They represent the specific properties and direction of the z-axis in three-dimensional space.