Question
Asked Sep 21, 2019
734 views
    The distance dd of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram. So the distance from P=(3,−4,5) to the line through the points A=(4,2,−2) and B=(−2,0,5) is
P
В
A
help_outline

Image Transcriptionclose

P В A

fullscreen
check_circle

Expert Answer

star
star
star
star
star
1 Rating
Step 1

Given,

           The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram.

help_outline

Image Transcriptionclose

P. В A

fullscreen
Step 2

Here, we have P = (3, −4, 5), A = (4, 2, −2) and B = (−2, 0, 5).

Now,

help_outline

Image Transcriptionclose

The component PA is b = (4 - 3,2 (-4),-2 - 5) = (1,6,-7) And AB a (-2 - 4,0 2,5- (-2) ) - (-6,-2, 7)

fullscreen
Step 3

Therefore, the distanc...

help_outline

Image Transcriptionclose

d laxb lal j k 6 2 7 6 -7 |(-6)2+(-2)2+72 li(14-42)-(42-7)+k(-36+2)| V36+4+49 |-28i-j35-34k| /36+4+49 /784+1225+1156 68 3165 V89 3156 89

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Other

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add