We want to find O(x,y,z) by using two known points P(2,3,5) and Q(1,2,2) and angle of POQ=60 degrees with plane E:1.15714286x+1.8547619y−z−2.86101191=0 and length OP=OQ. Is there any way to find it?

Glenn Hopkins

Glenn Hopkins

Answered question

2022-07-18

We want to find O ( x , y , z ) by using two known points P ( 2 , 3 , 5 ) and Q ( 1 , 2 , 2 ) and angle of P O Q = 60 degrees with plane E : 1.15714286 x + 1.8547619 y z 2.86101191 = 0 and length O P = O Q
Is there any way to find it?

Answer & Explanation

ab8s1k28q

ab8s1k28q

Beginner2022-07-19Added 17 answers

You have 3 conditions:
1). point O ( x , y z ) lies on plane E, so
1.15714286 x + 1.8547619 y z = 2.86101191
2). O P = O Q
( x 2 ) 2 + ( y 3 ) 2 + ( z 5 ) 2 = ( x 1 ) 2 + ( y 2 ) 2 + ( z 2 ) 2 .
This simplifies to
2 x + 2 y + 6 z = 29.
3). P O Q = 60 and O P = O Q so P O Q is equilateral. Thus
O Q 2 = P Q 2 ( x 1 ) 2 + ( y 2 ) 2 + ( z 2 ) 2 = 11.
The answer will not be unique.

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