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ENG1014 - MUM S2 2025 Weekly quiz 8
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Question textIn crystallography, the intersection of three non-coplanar crystallographic planes, each with high probability densities, will generally give the location of an atom in the crystal structure where they intersect each other at a point, as shown below. The equations of three such planes are given below:Plane 1: \(5x-2y-4z=6\) Plane 2: \(-x-2y+2z=4\) Plane 3: \(5x-2y+3z=2\) What is the location of the atom in \((x,y,z)\), to 3 decimal places? \(x\): Answer 1 Question 2[input] \(y\): Answer 2 Question 2[input] \(z\): Answer 3 Question 2[input]

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Step-by-Step Analysis
We are given three planes and asked to find the unique intersection point (x, y, z).
First, observe the equations:
Plane 1: 5x - 2y - 4z = 6
Plane 2: -x - 2y + 2z = 4
Plane 3: 5x - 2y + 3z = 2
A efficient way is to eliminate variables step by step. A convenient starting point is to eliminate x or y by subtracting Plane 1 from Plane 3, sin......Login to view full explanationLog in for full answers
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