How to Find the Normal Vector of the Second Plane?

[the_rising]

Hello everyone,

I posted this question before also but did not get the satisfactory answer. So I am posting the question again with more specifications. My question is --- Suppose we have two planes intersecting in one line. Let one plane's normal be [3,4,2] and other plane's normal be [a,b,c]. We know the angle between the two planes as 60 degrees. We know one point on the intersecting line, suppose (7,3,4). Now with this information in hand, can we find out the normal vector of second plane ie [a,b,c].
All the responses are welcome.

Regards,

 

[HallsofIvy]

This is not enough information. If the angle between the planes is 60 degrees then the angle between normal vectors is also 60 degrees. But there are an infinite number of (unit) vectors that make a 60 degree angle with [3,4,2]. Any vector on the cone making a 60 degree angle with [3,4,2] as its axis satisfies that.

 

[the_rising]

This is not enough information. If the angle between the planes is 60 degrees then the angle between normal vectors is also 60 degrees. But there are an infinite number of (unit) vectors that make a 60 degree angle with [3,4,2]. Any vector on the cone making a 60 degree angle with [3,4,2] as its axis satisfies that.

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Thanks for the info...
If we know two points on the line of intersection, then is it possible to find out the normal of the second plane ?

 

[Dr.Brain]

If the planes make angle of 60 degrees at the point of intersection , then the normals also make the same angle, this condition will give you an equation in a,b and c.
Secondly, the normal of any of the two planes will be prependicular to the line of intersection of two planes.You can find the line of intersection by subtracting one plane equation from other.This will give you one more equation in a,b and c.If the equation of planes is not given , use the point on the intersection-line given .

Now make a quadrilateral of which two angle are 90 degree, one is 60 degree , find the fourth one , using this and some geometry find the length of the normal (for which u need the a,b,c) , this gives you the third equation.Solve the three variables.

BJ

 

[Dr.Brain]

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Thanks for the info...
If we know two points on the line of intersection, then is it possible to find out the normal of the second plane ?

If you know two points on the line of intersection of two planes , you can derive the equation of the line , which will make your job easier.

BJ