What is the distance between the point (2, 3, 4) and the plane x + y + z = 10? (
Practice Questions
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What is the distance between the point (2, 3, 4) and the plane x + y + z = 10? (2022)
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Questions & Step-by-Step Solutions
What is the distance between the point (2, 3, 4) and the plane x + y + z = 10? (2022)
Step 1: Identify the point and the plane. The point is (2, 3, 4) and the plane equation is x + y + z = 10.
Step 2: Rewrite the plane equation in the form Ax + By + Cz + D = 0. Here, A = 1, B = 1, C = 1, and D = -10.
Step 3: Use the distance formula from a point (x0, y0, z0) to a plane Ax + By + Cz + D = 0, which is given by: Distance = |Ax0 + By0 + Cz0 + D| / √(A² + B² + C²).
Step 4: Substitute the values into the formula. For the point (2, 3, 4), we have x0 = 2, y0 = 3, z0 = 4.
