Find the distance from the point P(4, -3, 5) to the line given by x = 2 - 4t, y = 5 + 3t, z = 7 - t.

Question:

Find the distance from the point {eq}P(4, -3, 5) {/eq} to the line given by {eq}x = 2 - 4t {/eq}, {eq}y = 5 + 3t {/eq}, {eq}z = 7 - t {/eq}.

Distance from a Point to a Line:

To calculate this distance, we will do the following steps:

Step 1: We calculate a plane that passes through the point perpendicular to the given line.

Step 2: Intersect the plane with the line, obtaining an intersection point.

Step 3: The requested distance coincides with the distance between the initial point and the intersection point.

Answer and Explanation:

To calculate this distance:

First, we calculate a plane that passes through point P perpendicular to the given line:

Using the equation:

{eq}\pi ...

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Distance Formulas: Calculations & Examples

from Algebra I: High School

Chapter 3 / Lesson 10
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