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
lora16 [44]
3 years ago
12

Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).

Mathematics
1 answer:
topjm [15]3 years ago
3 0
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)

We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>

The vector product pq x pr gives a vector perpendicular to both pq and pr.  This vector is the normal vector of a plane passing through all three points
pq x pr
=
  i   j   k
-4 -2 -4
-3  5  1
=<-2+20,12+4,-20-6>
=<18,16,-26>

Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>

The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).

The equation of the required plane is therefore
Π :  9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π  :  9x+8y-13z=24

Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.

You might be interested in
I need help with this problem can you please show the work
AysviL [449]

Answer:

48 degrees

Step-by-step explanation:

inscribed angle is always equal to the measure of the arc

4 0
3 years ago
An 8 oz box of cocoa puffs costs $1.59 and a 2-pound box costs $6.79. which box is a better buy
VikaD [51]

Answer: 8 oz..

1 pound= 16oz if 8oz=1.59 so add it up 4 times 8+8+8+8= 32 which = 2 pounds total 8=1.59 8+8= 1.59x2=3.18 8+8+8=1.59x3=4.77 8+8+8+8/ 1.59x4= 6.36 so all of them eights will = up to 2 pounds and 8 is obviously less

Step-by-step explanation:

6 0
3 years ago
(Y+9)x2=42 find the cross products
sveta [45]
2y+18=42
2y=24
y=12
Hope this helps!
8 0
3 years ago
Please help!<br> I don't know how to read/answer the image
rusak2 [61]

Answer:

SAS

Step-by-step explanation:

SSS= Side Side Side

SAS= Side Angle Side

ASA= Angle Side Angle

SAA= Side Angle Angle

HL= Height Length

7 0
3 years ago
During a bike challenge, riders have to collect various colored ribbons. Each 1/2 mile they collect a red ribbon, each 1/8 mile
Oliga [24]
One red ribbon, 6 green ribbons and 3 blue ribbons total together would be 10 ribbons
3 0
3 years ago
Other questions:
  • Five different stores sell a bottle of water for one of the following prices:$1.45,$1.55,$1.85,$1.95,$1.45 what are the mean,med
    6·2 answers
  • HELP!!! PLEASE I WOULD APPRECIATE IT SO MUCH!!
    12·1 answer
  • Given an integer, how do you find it's opposite?
    7·1 answer
  • Karen is estimating how much flour she needs if each cake requires 2 2/6 cups of flour and she is making 3 cakes. Explain how ma
    12·1 answer
  • Answer these questions please: You don't need to plot the point just answer B &amp; C. Also every single coordinate plane is lik
    14·1 answer
  • Have even leader = 16.91 oz how many ounces are in 3 leaders
    5·2 answers
  • I am giving 100 points to whoever solves this first, I really need help please help!!!
    11·2 answers
  • Andrea needs a new air conditioning system for her house. An air conditioner needs to
    7·1 answer
  • A football stadium has 4,890 seats. There are 6 sections
    12·1 answer
  • What is the slope AND y-intercept to this equation: y=6x-8
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!