Final answer:
To determine parallel planes, rewrite the plane equations in standard form and compare the coefficients of x, y, and z. In this case, planes p1 and p4 are parallel as they have the same direction coefficients.
Step-by-step explanation:
To identify which of the planes are parallel, we must first write the equations of the planes in standard form. This form allows us to directly compare the coefficients of x, y, and z, which determine the planes' orientation. The standard form for the equation of a plane is Ax + By + Cz = D, where A, B, and C are the directional coefficients.
Let's rewrite plane equations:
1. p1: 4x + 8y - 4z = 12 --> x + 2y - z = 3 (divide the equation by 4)
2. p2: 5x - 15y +10z = 6 --> x - 3y + 2z = 1.2 (divide by 5)
3. p3: it's unreadable and needs to be clarified
4. p4: 2z = 2x + 4y - 6 --> x + 2y - z = -3 (divide by 2 and bring terms on one side)
Comparing the direction coefficients, we find that p1 and p4 have the same coefficients (with different constant terms), so they are parallel.
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