Which of the following is not a point on the plane with Cartesian equation `3x+2y-2z-4=0`? a) P(2,0,1) b) Q(2,3,4) c) R(1,1,1) d) S(0,3,1)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

In order to determine which point is not on the plane of the given equation , you must substitute the values given for each point. If the left side (L.S) is equal to the right side (R.S) then the point IS on the plane.

Example:
a) P(x,y,z) = P(2,0,1)

L.S

`=3(2)+2(0)-2(1)-4`

`= 6+0-2-4`

`=0`

L.S `=` R.S `=0`

This point P(2,0,1) therefore, is on the plane.

However, now try c) R(1,1,1)

L.S

`=3(1)+2(1)-2(1)-4`

`=3+2-2-4`

`=-1`

Here we see that L.S `!=` R.S

`:. ` The point that is not on the plane is R(1,1,1)

 

 

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial