?Let P be a point not on the line L that passes through the points Q and R. (a) Show

Chapter 12, Problem 45

(choose chapter or problem)

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

(a) Show that the distance d from the point P to the line L is

$d=\frac{|a \times b|}{|a|}$

Where $a=\overrightarrow{Q R}$ and $b=\overrightarrow{Q P}$.

(b) Use the formula in part (a) to find the distance from the point $P(1, 1, 1)$ to the line through $Q(0, 6, 8)$ and $R(ー1, 4, 7)$.

Equation Transcription:

$d=\frac{|a\times{}b|}{|a|}$

$a=\vec{QR}$

$b=\vec{QP}$

P(1, 1, 1)

Q(0, 6, 8)

R(ー1, 4, 7)

Text Transcription:

d=|a times b|/|a|

a=^rightarrow QR

b=^rightarrow QP

P(1, 1, 1)

Q(0, 6, 8)

R(ー1, 4, 7)

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