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
ipn [44]
3 years ago
5

Find symmetric equations for the line of intersection of the planes. z = 4x − y − 13, z = 6x + 5y − 13

Mathematics
1 answer:
MArishka [77]3 years ago
3 0
The intersection line of two planes is the cross product of the normal vectors of the two planes.

p1: z=4x-y-13 => 4x-y-z=13
p2: z=6x+5y-13 => 6x+5y-z=13
The corresponding normal vectors are:
n1=<4,-1,-1>
n2=<6,5,-1>

The direction vector of the intersection line is the cross product of the two normals, 
vl=
 i   j   k
4 -1 -1
6  5 -1
=<1+5, -6+4, 20+6>
=<6,-2,26>
We simplify the vector by reducing its length by half, i.e.
vl=<3,-1,13>

To find the equation of the line, we need to find a point on the intersection line.
Equate z:  4x-y-13=6x+5y-13 => 2x+6y=0 => x+3y=0.
If x=0, then y=0, z=-13 => line passes through (0,0,-13)

Proceed to find the equation of the line:
L: (0,0,-13)+t(3,-1,13)
Convert to symmetric form:
\frac{x-0}{3}=\frac{y-0}{-1}=\frac{z-(-13)}{13}
=>
\frac{x}{3}=\frac{-y}{1}=\frac{z+13}{13}

You might be interested in
A store is giving a $10 coupon th every 7tgh person, and a $25 coupon to every 18th person, Which person will be the first to ge
elixir [45]

Answer:

126th

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Huntly Billings bought a $1,000 bond for $1,050. What was the quotation of the bond?
dmitriy555 [2]

Step-by-step explanation:

1000 for 50 is store profit

7 0
2 years ago
How many terms in the<br> sequence are less than 100?
Vaselesa [24]

Answer:

99

Step-by-step explanation:

Since given, < 100.

So,

100 - 1 = 99

5 0
2 years ago
your dad tells you he will pay you 6 dollars a hour for the six seconds it takes you to wash your hands before dinner. How much
Lostsunrise [7]
You made 2 cents if you round down
3 0
3 years ago
Convert 120 kilometers per hour to meters per minute.
svlad2 [7]

Answer:

2000 meters per minute

Step-by-step explanation:

120 kilometers per hour=2000 meters per minute

5 0
3 years ago
Read 2 more answers
Other questions:
  • At the grocery Store,ayla buys 1 one third pounds of ground turkey.Tasha buys 2 times as much ground turkey as ayla. How much gr
    7·1 answer
  • Determine the solution and the reasoning that justifies the solution to the systems of equations.
    9·1 answer
  • Can you find the slope of the line. I have to turn this in today lol
    6·1 answer
  • I need help asapp:) thank youu
    10·2 answers
  • I need step by step please
    9·1 answer
  • Like segment AB is divided by point C in the ratio of 1:3
    12·1 answer
  • The total cost of eight pens and five mechanical pencils is $8.55. The cost of each pencil is $0.35 cents. Let the cost of a pen
    5·1 answer
  • Answer please I’m like really bad in math hahaha
    12·2 answers
  • FULL EXPLANATION PLEASE<br> WILL MARK BRAINLIST!! :)
    12·1 answer
  • URGENT PLEASE HELP!!
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!