If two lines are perpendicular to the same line, then they are parallel... true??

Question

Can you help me figure these out?

They are answered with true or false, but please help include proof , or make one of your own or take a picture of one that you drew...

1. Only one plane can pass through three noncollinear points.

true or false?

2. If two lines are perpendicular to the same line, then they are parallel.

true or false? i think it's true....

3. If a line and a plane have no points in common, then they are parallel.

true or false?

4. If three random planes intersect (no two are parallel and all three do not share the same line), then they divide space into six parts.

true or false?

Answer 1

PROBLEM 1:

True, 3 non-collinear points define one unique plane.

PROBLEM 2:

False, I have at least two counterexamples.  One case would be that you have the exact same line.  The other case would be that the lines go off in different directions in 3-D and are therefore skew.

PROBLEM 3:

True

PROBLEM 4:

False, you can have up to eight regions.  (Think of the 3 planes associated with the x, y and z planes where they are all at right angles to each other.)

Answer 2

only if they are in the same plane  and also not the identical lines

the x y z axis are all perp to eachother

1. Only one plane can pass through three noncollinear points.

true

2. If two lines are perpendicular to the same line, then they are parallel.

false

3. If a line and a plane have no points in common, then they are parallel.

true

4. If three random planes intersect (no two are parallel and all three do not share the same line), then they divide space into six parts.

false

Answer 3

1. Only one plane can pass through three noncollinear points.

FALSE- noncollinear points are points that do not all share the same line or plane, so it would take two planes to pass through all 3 noncollinear points.

2. If two lines are perpendicular to the same line, then they are parallel.

TRUE- look at these two lines perpendicular to another line:

______________________________________...

Top and bottom lines parallel. |

_________________________|____________...

3. If a line and a plane have no points in common, then they are parallel.

TRUE- any two things that are parallel never intersect, and the only way to have one point in common is to be intersecting.

4. If three random planes intersect (no two are parallel and all three do not share the same line), then they divide space into six parts.

FALSE- they divide it into seven parts:

...........|./...............

______|/____________

........../|..................

........./.|................

......./...|..................

You can basically see the seven different sections made by the planes.