What is the distance between the parallel planes 2x + 3y - z = 5 and 2x + 3y - z

What is the distance between the parallel planes 2x + 3y - z = 5 and 2x + 3y - z = 10? (2021)

What is the distance between the parallel planes 2x + 3y - z = 5 and 2x + 3y - z = 10? (2021)

Step 1: Identify the equations of the parallel planes. The first plane is 2x + 3y - z = 5 and the second plane is 2x + 3y - z = 10.
Step 2: Recognize that the distance between two parallel planes can be calculated using the formula: Distance = |d1 - d2| / √(A² + B² + C²), where d1 and d2 are the constant terms from the plane equations.
Step 3: Identify d1 and d2 from the plane equations. Here, d1 = 5 and d2 = 10.
Step 4: Calculate the absolute difference between d1 and d2: |5 - 10| = 5.
Step 5: Identify the coefficients A, B, and C from the plane equations. Here, A = 2, B = 3, and C = -1.
Step 6: Calculate A² + B² + C²: 2² + 3² + (-1)² = 4 + 9 + 1 = 14.
Step 7: Calculate the square root of the sum: √(14).
Step 8: Substitute the values into the distance formula: Distance = 5 / √(14).

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