Geometry

3D Coordinate Geometry

3D Coordinate Geometry - Parallel Planes

         

Which of the following is/are true regarding three planes α,β,\alpha,\beta, and γ\gamma in the coordinate space?

I. If α: a1x+b1y+c1z+d1=0\alpha:~a_1x+b_1y+c_1z+d_1=0 and β: a2x+b2y+c2z+d2=0\beta:~a_2x+b_2y+c_2z+d_2=0 are parallel, then a1=a2, b1=b2,a_1=a_2,~b_1=b_2, and c1=c2.c_1=c_2.

II. If αβ\alpha\parallel\beta and βγ,\beta\parallel\gamma, then αγ.\alpha\parallel\gamma.

III. If αβ\alpha\bot\beta and βγ,\beta\bot\gamma, then αγ.\alpha\parallel\gamma.

If the two planes 18x+15y6z+1=018x+15y-6z+1=0 and ax+by+2z+1=0ax+by+2z+1=0 are parallel, what is the value of ab?ab?

What is the distance between the two planes α: 2xy+3z+4=0\alpha:~2x-y+3z+4=0 and β: 2xy+3z24=0?\beta:~2x-y+3z-24=0?

What is the equation of the plane that is parallel to 3x+2y+z1=03x+2y+z-1=0 and passes through the point P=(5,1,5)?P=(-5,1,-5)?

Which of the following planes is parallel to x2y+3z4=0?x-2y+3z-4=0?

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