Find the distance between the parallel planes 2x + 3y + z = 5 and 2x + 3y + z =
Practice Questions
Q1
Find the distance between the parallel planes 2x + 3y + z = 5 and 2x + 3y + z = 10. (2022)
5
10
√14
√10
Questions & Step-by-Step Solutions
Find the distance between the parallel planes 2x + 3y + z = 5 and 2x + 3y + z = 10. (2022)
Step 1: Identify the equations of the two parallel planes. The first plane is 2x + 3y + z = 5 and the second plane is 2x + 3y + z = 10.
Step 2: Recognize that the general form of a plane is Ax + By + Cz = d, where A, B, C are the coefficients of x, y, z respectively, and d is a constant.
Step 3: From the equations, identify A, B, C, and the constants d1 and d2. Here, A = 2, B = 3, C = 1, d1 = 5, and d2 = 10.
Step 4: Use the formula for the distance between two parallel planes: Distance = |d1 - d2| / √(A² + B² + C²).
Step 5: Calculate the absolute difference between d1 and d2: |5 - 10| = 5.
Step 7: Substitute the values into the distance formula: Distance = 5 / √14.
Step 8: The final answer is the distance between the two parallel planes.
Distance Between Parallel Planes – The formula for the distance between two parallel planes of the form Ax + By + Cz = d is given by |d1 - d2| / √(A² + B² + C²), where d1 and d2 are the constant terms of the planes.
