Question

The equation of the plane which is parallel to \[xy\] plane and cuts intercept of length 3 from the \[z\] axis
A. \[x = 3\]
B. \[y = 3\]
C. \[z = 3\]
D. \[x + y + z = 3\]

Answer 1

Hint: First see which plane is parallel to \[xy\] plane. Then according to the intercept given, find out the coordinates of the parallel plane. Using the coordinate and the condition mentioned, an equation for the plane can be found.

Complete step-by-step answer:
Given \[z\] intercept is 3 and the it is parallel to \[xy\] plane

Therefore, the coordinates of \[z\] are \[\left( {0,0,3} \right)\]
Plane parallel to \[xy\] axis is obviously \[z\] plane
Let the equation of the plane be \[z = k\]
Hence, \[k = 3 \Rightarrow z = 3\] is the equation of the plane.
Therefore, \[z = 3\] is the equation of the plane which is parallel to the \[xy\] plane and cuts the intercept of length 3 from the \[z\] axis.
Thus, the correct option is C. \[z = 3\]

Note: In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space.
Always remember that,
Plane parallel to x-axis has the equation of the form \[by + cz = d\]
Plane parallel to y-axis has the equation of the form \[ax + cz = d\]
Plane parallel to z-axis has the equation of the form \[ax + by = d\]