We want to find O ( x , y , z ) by using two...

Glenn Hopkins

Glenn Hopkins

Answered

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

Expert

2022-07-19Added 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.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?