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
Fantom [35]
3 years ago
11

Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. What is the distance between the origin and

the plane?
Mathematics
1 answer:
Elenna [48]3 years ago
3 0

Answer:

The equation is:

(1/a)x + (1/b)y + (1/c)z = 1

Step-by-step explanation:

The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:

<0 - a, b - 0, 0 - 0>

<-a, b, 0> .....................(1)

The direction vector between (0, 0, c) and (0, b, 0) is given as:

<0 - 0, b - 0, 0 - c>

= <0, b, -c> .....................(2)

To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).

Doing this, we have:

<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>

To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:

(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0

(bc)x + (ac)y + (ab)z = (ac)b

Dividing both sides by abc, we have:

(1/a)x + (1/b)y + (1/c)z = 1

You might be interested in
Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and pro
viva [34]

Answer:

9600 m2

Step-by-step explanation:

6 0
3 years ago
Help ! i’ll give brainliest
Y_Kistochka [10]

Answer:

5p+s

Step-by-step explanation:

five friends jumping for one hour

4 0
2 years ago
Use the compound interest formula to determine the final value of the given amount.
CaHeK987 [17]

Answer:

342.22$

Step-by-step explanation:

7 0
2 years ago
1/3 (12 - 24v) = -2(4v -2)
ANEK [815]
Opening brackets gives;
4-8v=-8v+4
Putting like terms together;
4-4=-8v+8v
0=0
There is no solution thus.
3 0
3 years ago
Solve the following literal equation for r in
grandymaker [24]
400 because I said so and u are asking me is here is the answer
8 0
2 years ago
Other questions:
  • A cube is numbered 1 through 6. If the cube is rolled twice, how many of the possible outcomes will have two even numbers?
    14·1 answer
  • Select the function that represents the simple interest formula.
    5·2 answers
  • N<br> What is the range of the function f(x) = -2(6") + 3?
    9·1 answer
  • Which two of the following are not characteristics of surveys?
    15·1 answer
  • PLEASE help me ! 10 points + brainliest :))
    5·1 answer
  • Which of the following is equivalent to 2 2/5 ?
    14·2 answers
  • PLS HELPPPPP Find the perimeter of AXYZ. *
    13·2 answers
  • I REALLY NEED HELp!!!!!!!!
    10·1 answer
  • Lindy works at a pizza restaurant and gets a 10% employee discount. She knows that if she orders d drinks and a medium pizza wit
    13·1 answer
  • Jose bout 9 movie tickets for a total of $54 adult tickets cost $8 is an adult child ticket cost $3.50 each. How many adult tick
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!