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Let P be a point not on the line L that passes through the points Q and R. The distance d from...

Question:

Let {eq}P {/eq} be a point not on the line {eq}L {/eq} that passes through the points {eq}Q {/eq} and {eq}R {/eq}. The distance {eq}d {/eq} from the point {eq}P {/eq} to the line {eq}\displaystyle L {/eq} is {eq}\displaystyle d = \frac {|a \times b|} {|a|} {/eq} where {eq}\displaystyle a = QR {/eq} and {eq}\displaystyle b = QP {/eq}.

Use the above formula to find the distance from the point to the given line. {eq}\displaystyle (0,\ 3,\ 3);\ x = 2 t,\ y = 4 - 2 t,\ z = 3 + t {/eq}.

The Distance Between A point And A line :

Let {eq}P {/eq} be a point not on the line {eq}L {/eq} that passes through the points {eq}Q {/eq} and {eq}R {/eq}.

The distance {eq}d {/eq} from the point {eq}P {/eq} to the line {eq}\displaystyle L {/eq} is {eq}\displaystyle d = \frac {|a \times b|} {|a|} {/eq} where {eq}\displaystyle a = QR {/eq} and {eq}\displaystyle b = QP {/eq}.

Answer and Explanation:

Using the values {eq}t = 0 and t = 1, {/eq}

the two points

{eq}Q=\left ( 0,4,3 \right )\\ R=\left ( 2,2,4 \right ) P=\left ( 0,3,3 \right...

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How to Find the Distance Between a Point & a Line

from FTCE Mathematics 6-12 (026): Practice & Study Guide

Chapter 30 / Lesson 5
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