In a three-dimensional Cartesian coordinate system, the position of a point is typically described using three coordinates that represent its location along the x, y, and z axes. These coordinates are usually written in the following standard notation:
[tex]\((x, y, z)\)[/tex]
Let's analyze the given options to determine which one correctly represents this standard notation:
A. [tex]\((x, y, v)\)[/tex] - This option is incorrect because the third coordinate should be [tex]\(z\)[/tex], not [tex]\(v\)[/tex].
B. [tex]\(x, y, z\)[/tex] - This option is also incorrect because the coordinates are not enclosed in parentheses, which is standard for representing a point.
C. [tex]\((x, y, z)\)[/tex] - This option correctly represents a point in a three-dimensional Cartesian coordinate system, with each coordinate enclosed within parentheses.
D. [tex]\((w, x, y)\)[/tex] - This option is incorrect because the coordinates should be [tex]\(x, y,\)[/tex] and [tex]\(z\)[/tex]. The third coordinate is wrong here, and the order is out of standard form.
From the options provided, the correct standard notation for a point in a three-dimensional Cartesian coordinate system is:
C. [tex]\((x, y, z)\)[/tex]
