1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ozzi
3 years ago
6

Let T be the plane-2x-2y+z =-13. Find the shortest distance d from the point Po=(-5,-5,-3) to T, and the point Q in T that is cl

osest to Po. Use the square root symbol 'where needed to give an exact value for your answer. d 0 0 (0, 0, 0)
Mathematics
1 answer:
GaryK [48]3 years ago
7 0

Answer:

d=10u

Q(5/3,5/3,-19/3)

Step-by-step explanation:

The shortest distance between the plane and Po is also the distance between Po and Q. To find that distance and the point Q you need the perpendicular line x to the plane that intersects Po, this line will have the direction of the normal of the plane n=(-2,-2,1), then r will have the next parametric equations:

x=-5-2\lambda\\y=-5-2\lambda\\z=-3+\lambda

To find Q, the intersection between r and the plane T, substitute the parametric equations of r in T

-2x-2y+z =-13\\-2(-5-2\lambda)-2(-5-2\lambda)+(-3+\lambda) =-13\\10+4\lambda+10+4\lambda-3+\lambda=-13\\9\lambda+17=-13\\9\lambda=-13-17\\\lambda=-30/9=-10/3

Substitute the value of \lambda in the parametric equations:

x=-5-2(-10/3)=-5+20/3=5/3\\y=-5-2(-10/3)=5/3\\z=-3+(-10/3)=-19/3\\

Those values are the coordinates of Q

Q(5/3,5/3,-19/3)

The distance from Po to the plane

d=\left| {\to} \atop {PoQ}} \right|=\sqrt{(\frac{5}{3}-(-5))^2+(\frac{5}{3}-(-5))^2+(\frac{-19}{3}-(-3))^2} \\d=\sqrt{(\frac{5}{3}+5))^2+(\frac{5}{3}+5)^2+(\frac{-19}{3}+3)^2} \\d=\sqrt{(\frac{20}{3})^2+(\frac{20}{3})^2+(\frac{-10}{3})^2}\\d=\sqrt{\frac{400}{9}+\frac{400}{9}+\frac{100}{9}}\\d=\sqrt{\frac{900}{9}}=\sqrt{100}\\d=10u

You might be interested in
What does it mean when two things are opposites?
svetoff [14.1K]

Answer:

Step-by-step explanation:

differences

6 0
3 years ago
Read 2 more answers
A student can type on average 210 words in three minutes how long would it take for them to type 1001 word paper
Vlada [557]
30 minutes I believe
8 0
3 years ago
Read 2 more answers
(can someone help??) <br> −12x+8=6x−12−13/2x
worty [1.4K]

Answer:

t

Step-by-step explanation:

h

4 0
3 years ago
3.01 repeating as a mixed number in simplist <br> form
ziro4ka [17]

Answer:

3 1/100 is the answer.

Step-by-step explanation:

5 0
3 years ago
Simplify 14a over 15 Plus 2a + 36 over 5​
Yuliya22 [10]

Answer:

(20a+108)/15

Step-by-step explanation:

First find LCM of the denominators. U will find it to be 15

Then calculate the number like this.

[(14a)×1/15×1]+[(2a+36)×3/5]

[(14a/15)]+[(6a+108)/15

(14a+6a+108)/15

(20a+108)/15

5 0
3 years ago
Other questions:
  • Please help and dont just say hope you get it​
    14·1 answer
  • The measure of MKJ is 80°. After analyzing the diagram, Janelle concludes that is an angle bisector.
    15·2 answers
  • Please please please help me !!
    8·1 answer
  • How do you graph y=-x-2?
    10·1 answer
  • A rectangular field is 24 yards in length and 81 feet in width.
    12·1 answer
  • i need help please i don’t understand this question katie murphy poop poop oh no no idea why are y’all going on
    9·2 answers
  • Kiki has read
    8·1 answer
  • I need help please help me ​
    13·1 answer
  • GOD BELIEVES YOU CAN HELP ME
    9·2 answers
  • A client named Tommy wants us to prepare a 3300-word Marketing Report + Poster. If a task is quantifiable by word count, we char
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!