(1 point) Consider the following geometry problems in 3-space Enter Tor F depend

Question

(1 point) Consider the following geometry problems in 3-space Enter Tor F depending on whether the statement is true or false. (You must enter Tor F - True and False will not work.) 1. Two planes orthogonal to a line are parallel 2. Two planes either intersect or are parallel 3. Two planes parallel to a line are parallel 4. Two planes orthogonal to a third plane are parallel 5. Two planes parallel to a third plane are parallel 6. A plane and a line either intersect or are parallel 7. Two lines orthogonal to a third line are parallel 8. Two lines either intersect or are parallel 9. Two lines parallel to a plane are parallel 10. Two lines parallel to a third line are parallel 11. Two lines orthogonal to a plane are parallel

Explanation / Answer

1. FALSE

Let the line be x-axis. Then xy plane is orthogonal to the line. The direction vector on xy plane is in direction of z-axis. xz plane is orthogonal to the line. The direction vector on xy plane is in direction of y-axis. So, the 2 planes are orthogonal to the line but they are not parallel to each other.

2. TRUE

3. TRUE

4. FALSE

xy plane and xz plane are orthogonal to yz plane. But they (zy and xz) are not parallel to each other.

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