Abel H.

asked • 06/17/13# which fact is not sufficient to show that planes R and S are perpendicular?

FJ is contained in plane R, BC and DE are contained in plane S, and FJ, BC, and DE intersect at A.

its hard for me

## 4 Answers By Expert Tutors

Stanton D. answered • 11/27/13

Tutor to Pique Your Sciences Interest

Vladimir B. answered • 07/03/13

Identify Hidden Active Causes. Imagine then Verify.

Just to add to the straight points made by my colleagues in Hallandale, FL and Franklin, TN ...

... **I wish there were an easier way to make the points below** ... Also, one has to strain their 3D imagination to see what I'm talking about ... please better employ right angle rulers and cardboard sheets ...

Making a long story short, plane R would be perpendicular onto plane S ... and vice-versa ...

... **IF** { { a 90° angle would exist between **either** FJ & BC **or** FJ & DE } **and** { of the 2 segments perpendicular to each other ... { one of the segments would be perpendicular onto the {R∩S} straight line } ... **and** ... { the other segment NOT being parallel/ included into the {R∩S} straight line } } } ...

... which tells us that ...

1. to assess 2 planes (R & S) as perpendicular onto each other, the value of some angles (in this case between any of the extensions of FJ, BC, DE intersecting in A) must be given ;

2. but such angles cannot be defined unless we know more about the orientation of FJ within plane R and the orientations of BC & DE within plane S ; specifically it is the orientation of these 3 segments defined with respect to the 2 plane {R∩S} straight line intersection that **would make the difference**.

I'm not sure if this helped.

Rafael V.

Agree

Agree ......

In order for them to be perpendicular the vector normal to a plane must be parallel to the other plane

So either FJ have to be parallel to the normal vector at plane S

or ( BC or DE ) be parallel to the normal vector at plane R

07/03/13

Nataliya D. answered • 06/17/13

Patient and effective tutor for your most difficult subject.

So far, we have only one fact: FJ, BC, and DE intersect at A. Other two, "FJ is contained in plane R, BC and DE are contained in plane S", are "subfacts" .

The fact, that FJ, BC, and DE intersect at point A is not sufficient to show that planes R and S are perpendicular.

If we will know that FJ is perpendicular to BC or DE we will say that plane R | to plane S.

P.S. Abel, make sure you copy the problem completely.

Xavier J.

*If we will know that FJ is perpendicular to BC or DE we will say that plane R | to plane S. *

I'm not so sure we can automatically conclude that R and S are perpendicular if FJ were perpendicular.

Based off the info provided in the problem we have to assume FJ is on R and BC and DE are on S. This however does not mean BC, DE, or FJ cannot be the line of intersection of the 2 planes. Say we let DE be the line of intersection (DE will still be on the plane S) then the line FJ could be perpendicular to DE and R not be perpendicular to S.

The only way to ensure the 2 planes are perpendicular is to show that a line on either plane is perpendicular to the other plane.

06/17/13

Rollin W. answered • 06/17/13

Latin and Greek Tutoring in Nashville and Surrounding Area

As according to these two facts, R could rotate 360 degrees in both directions (Up/Down, Left/Right). Does this help?

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Nataliya D.

The problem says:

1. FJ is contained in plane R.

2. BC and DE are contained in plane S.

3. Point

Ais contained in plane R and in plane S.Rest is

- maybe ...

- might be ...

- could be ...

In other words, are not sufficient facts.

06/17/13