Question

Which statement is true of every plane in three-dimensional space?

Every plane must have three intercepts.


A plane can have no intercepts.


A plane has at least one intercept.


Every plane must have at least two intercepts.

Answer 1

Every plane must have three intercepts.

proof, every point P in a plane in three-dimensional space is written as P=(x, y, z), x, y and z are intercepts.

Answer 2

option A is correct.(Every plane must have three intercepts.)

Explanation:

" Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the term dimension "

The intercept form of the equation of plane in 3-D is given by:

`(x)/(l)+(y)/(m)+(z)/(n)=1`

Where l,m,n are intercepts of x,y,z axes and a plane respectively.

Hence, we require all the three intercepts of a every plane.

Hence, option A is correct.