Find the equation of the plane passing through the intersection of planes 2x + 3y – z = – 1 and x + y – 2z + 3 = 0 and perpendicular to the plane 3x – y – 2z = 4. Also find the inclination of this plane with xy-plane.
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we must first find the 2 other points on the plane. When z=0:
x + y = 22x - y = 13x = 3 -> x = 1, y = 1thus the point is ( 0,7/2,3/2).
Let a be the vector from ( -1, 2, 1 ) to ( 1, 1, 0 ):
a= <0- (-1) , 7/2 - 2, 3/2 - 1 > = < 1, 3/2, 1/ 2 >
The general equation for a plane is:1 (x + 1 ) - 2 ( y - 2 ) + 4 ( z - 1 ) = 0x - 2y + 4z = -1by: nl
we must first find the 2 other points on the plane. When z=0:
x + y = 22x - y = 13x = 3 -> x = 1, y = 1thus the point is ( 0,7/2,3/2).
Let a be the vector from ( -1, 2, 1 ) to ( 1, 1, 0 ):
a= <0- (-1) , 7/2 - 2, 3/2 - 1 > = < 1, 3/2, 1/ 2 >
The general equation for a plane is:1 (x + 1 ) - 2 ( y - 2 ) + 4 ( z - 1 ) = 0x - 2y + 4z = -1by: nl
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