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
OLEGan [10]
3 years ago
15

Find an equation of the plane. The plane that passes through the line of intersection of the planes x − z = 3 and y + 4z = 1 and

is perpendicular to the plane x + y − 4z = 4
Mathematics
1 answer:
Nata [24]3 years ago
3 0

Answer:

• 3x +y +z = 10

Step-by-step explanation:

The cross product of the normals of the intersecting planes will give a vector that is parallel to the line of intersection.

(1, 0 -1) × (0, 1, 4) = (1, -4, 1) . . . . using an appropriate calculator

Since this line is in the desired plane, it will be perpendicular to the desired plane's normal vector. The reference perpendicular plane likewise has its normal vector perpendicular to that of the desired plane. Hence the normal vector of the desired plane is perpendicular to both (1, -4, 1) and (1, 1, -4). It can be found from the cross product of these:

(1, -4, 1) × (1, 1, -4) = (15, 5, 5)

We can divide this by 5 to find our desired plane's normal vector: (3, 1, 1). To finish the equation of our plane, we need to know a point on the line of intersection. If we suppose z=0 at that point, then the remaining coordinates are ...

x -0 = 3 ⇒ x=3

y+4·0 = 1 ⇒ y=1

Using point (3, 1, 0) to find the constant in our plane's formula

3x +y +z = constant

we see it is ...

3·3 +1·1 +1·0 = constant = 10

The equation of the desired plane is ...

3x +y +z = 10

You might be interested in
231 ( 40 + 15 ) = 231 x 40 + ------------ x -----------<br><br> which property is this
a_sh-v [17]

Answer:

12705

Step-by-step explanation:

The problem could be solved in two different methods:

1:

231×(55)=12705

2.

231×40+231×15=9240+3465=12705

6 0
2 years ago
You've purchased a lottery ticket and your numbers are 5-3-1. A lottery official randomly selects three balls from a set of eigh
Inessa05 [86]

Answer:

1 out of 336 chance

Step-by-step explanation:

Since you picked three numbers, you are going to put three blanks.

What to do in this situation is to have _ _ _. Since there are numbers 1-8, what you want to do is take the three biggest numbers and multiply them together. in this case, they would be 8-7-6. Multiply that and you get 336.

8 0
3 years ago
30 POINTS<br><br> why are 3/4 and 6/8 equivalent
umka21 [38]

3/4 and 6/8 are equal and this is right I believe

4 0
3 years ago
Simplify -3x^2-5x^2(4x^3-x^2)2
PSYCHO15rus [73]

Let's simplify step-by-step.

−3x2−5x2(4x3−x2)(2)

Distribute:

=−3x2+−40x5+10x4

Answer:

=−40x5+10x4−3x2

8 0
3 years ago
Why do you change the sign when subtracting a negative number?
natulia [17]
This is because minus times minus is equals plus so the sign must change

5 0
3 years ago
Read 2 more answers
Other questions:
  • Which functions have real zeros at 1 and 4? Check all that apply.
    15·2 answers
  • Choose the correct classification of x6 + 3x3 by number of terms and by degree
    8·2 answers
  • can someone please help me I have a ton of math work and I struggle with it so hard. I'll give extra points
    6·2 answers
  • The ratio of the lengths of two
    11·1 answer
  • What is the mean of 3,4.5,6.5,8,8.5,10
    7·1 answer
  • How do I solve this system of equations? Help ASAP!<br><br> 2x+8y=6<br> -5x-20y=-15
    6·1 answer
  • a marathon runner ran the first 3 miles in 17.2minutes if she continues running at this pace how long will it take her to run th
    8·1 answer
  • 5. Miguel has an after-school job. He works
    5·1 answer
  • 7th grade math help!!
    14·2 answers
  • What is the solution to this system of equations?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!