Geometry

3D Coordinate Geometry

3D Coordinate Geometry - Intersection of Planes

         

State the relationship between the following two planes: −x+3y−z=2x−4y+z=2.\begin{aligned} -x + 3y -z &= 2 \\ x - 4y + z &= 2. \end{aligned}

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by Brilliant Staff

What is the volume of the tetrahedron formed by the plane 6x+3y+4z−72=0 6x + 3y + 4z - 72 = 0 and the three coordinate planes?

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If the following planes all intersect at the same line, what is the value of a+b: a+ b: P1:3x+ay+2z−2=0P2:2x+by−2z+a=0P3:3x−y+2z+b=0? \begin{aligned} P_1 &: 3x + ay + 2z -2 =0 \\ P_2 &: 2x + by - 2z + a = 0 \\ P_3 &: 3x - y + 2z + b = 0? \end{aligned}

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State the relationship between the following two planes: 2x−y+2z=−5x−3y+4z=3.\begin{aligned} 2x - y + 2z &= -5 \\ x - 3y + 4z &= 3. \end{aligned}

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by Brilliant Staff

State the relationship between the planes: 3x+y−2z=−4−6x−2y+4z=1.\begin{aligned} 3x + y - 2z &= -4 \\ - 6x - 2y + 4z &= 1. \end{aligned}

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by Brilliant Staff
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