Pre-U Vector Question

Yoshimineb

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Feb 6, 2018
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4
Hello,

I'm struggling with the question below.

The plane with equation 2x + 2y z = 5 is denoted by m.
Relative to the origin O, the points A has coordinate (1, 2, 1) which is in m.A second plane p is parallel to m and nearer to O.
The perpendicular distance between the planes is 1.Find the equation of p, giving your answer in the form ax + by + cz = d.





I found that plane p has an equation in the form of 2[FONT=&quot]x[/FONT]+2[FONT=&quot]y[/FONT][FONT=&quot]z[/FONT]=[FONT=&quot]k but can't find the value k.

I appreciate your help.[/FONT]
 

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    Screen Shot 2018-02-17 at 10.18.06.jpg
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The plane with equation 2x + 2y z = 5 is denoted by m.
Relative to the origin O, the points A has coordinate (1, 2, 1) which is in m. A second plane p is parallel to m and nearer to O.
The perpendicular distance between the planes is 1. Find the equation of p, giving your answer in the form ax + by + cz = d.

I found that plane p has an equation in the form of 2x+2yz=k but can't find the value k.

I appreciate your help.

Is the picture meant to be related??

One thing to do is to find the distance from A to your new plane, and set that distance equal to 1. Then you can solve for k.

Another is to find the distance from the origin to each of the two planes, and set the difference to 1. That may be easier, but doesn't use point A, and I expect they had a reason for mentioning it.

There are probably many more ways, depending on what you have learned about the distance between planes and/or points. What formulas do you have?
 
Is the picture meant to be related??

One thing to do is to find the distance from A to your new plane, and set that distance equal to 1. Then you can solve for k.

Another is to find the distance from the origin to each of the two planes, and set the difference to 1. That may be easier, but doesn't use point A, and I expect they had a reason for mentioning it.

There are probably many more ways, depending on what you have learned about the distance between planes and/or points. What formulas do you have?

Thank you for your reply,Dr.Peterson.

Sorry, the picture is not related to the question.

I used the easier method you mentioned to find the answer.



Thank you for your help.
 
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