# 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 ...

See full answer below.

Become a Study.com member to unlock this answer! Create your account

View this answer#### Learn more about this topic:

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Explore our homework questions and answer library

#### Our tutors are standing by

Ask a study question and one of our experts will send you an answer within hours.

To ask a site support question, click here

### Your question has been submitted!

When your answer is ready, it will appear on your Dashboard.

New! Get a text message when your answer is ready

Get Text AlertsNew! Get a text message when your answer is ready

Thanks! We'll text you when your answer is ready!