Posted by Alex on .
Someone please explain these!
The angle between two planes is defined as the angle between their normals. Determine the angle theta between 0 and 90 degrees between the given planes.
a) 2x+3yz+9 = 0 and x+2y+4 = 0

If the positive zaxiz points up, show that the line x=0, y=t, z=2t is parallel to and below the plane 2x10y+5z1 = 0.

Find an equation for the set of points P(x,y,z) that are equidistant from the points A(1,2,3) and B(4,0,1)

Math 
Reiny,
Love these kind of questions.
1. normals are (2,3,1) and (1,2,0)
a∙b = │a││b│cosß
2+6+0 = (√14)(√5)cosß
cosß=8/√70
ß will be the angle between the normals, can you take it from here?
2. The line has direction (0,1,2) and the plane has a normal of (2,10,5)
take the dot product.
If the normal is perpendicular to the line, shouldn't the line be paralle to the plane?
3. vector AB = (3,2,2)
this would be a normal to the plane, so the equation of the plane is
3x  2y  2z = C
Shouldn't this plane pass through the midpoint of AB ??
I am sure you can take it from there.