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
AlekseyPX
3 years ago
6

Determine as a linear relation in x, y, z the plane given by the vector function F(u, v) = a + u b + v c when a = 2 i − 2 j + k,

b = i + 2 j + 3 k, and c = 2 i + j + 2 k .
Mathematics
1 answer:
Ostrovityanka [42]3 years ago
3 0

Answer:

2x - y - 3z = 0

Step-by-step explanation:

Since the set

{i, j}  = {(1,0), (0,1)}

is a base in \mathbb{R}^2

and F is linear, then

<em>{F(1,0), F(0,1)}  </em>

would be a base of the plane generated by F.

F(1,0) = a+b = (2i-2j+k)+(i+2j+k) = 3i+2k

F(0,1) = a+c = (2i-2j+k)+(2i+j+2k) = 4i-j+3k

Now, we just have to find the equation of the plane that contains the vectors 3i+2k and 4i-j+3k

We need a normal vector which is the cross product of 3i+2k and 4i-j+3k

(3i+2k)X(4i-j+3k) = 2i-j-3k

The equation of the plane whose normal vector is 2i-j-3k and contains the point (3,0,2) (the end of the vector F(1,0)) is given by

2(x-3) -1(y-0) -3(z-2) = 0

or what is the same

2x - y - 3z = 0

You might be interested in
If rectangle A has a length and width that are z times the length and width of rectangle B, which of the following is true?
coldgirl [10]
The answer is A the perimeter of rectangle A is z times the perimeter of rectangle B
6 0
3 years ago
Solve F(x) for the given domain. <br> F(x) = x ^2 + 3x - 2 <br> F(3) = <br> 13<br> 16<br> 40
olchik [2.2K]
F(3) = 16, you simply plug in 3 for x to find the answer.
6 0
3 years ago
0.42 - 4) = 0.24 + 7)
Ronch [10]

Answer:

im sorry if not but i think its 7.24

Step-by-step explanation:

8 0
2 years ago
Just fill out the explanation on why it's 6?
g100num [7]

Answer: I subtracted 8 from both sides then divided 3 on both sides

Step-by-step explanation: welcome

8 0
3 years ago
Read 2 more answers
The opposite sides of a parallelogram are always sometimes or never congruent
KengaRu [80]
Always congruent due to the way the shape is built
6 0
3 years ago
Read 2 more answers
Other questions:
  • According to the U.S. Census Bureau (2016), a substantial pay gap still exists. The average American man, with an advanced colle
    5·1 answer
  • Given f(x) =5 - 3x, if f(x) = -19, find x
    8·1 answer
  • Find the product and simplify your answer. -n(-2n4+9n-5)​
    8·1 answer
  • Chen check the temperature at Dawn and at dusk every day for a week for a science project. How many observations does he make?
    11·2 answers
  • Whats 2+2-2-2-2-2+22+2-2+22222-2342122222+98765456789
    12·2 answers
  • If (x^2+1)/x = 7 find x^2+(1/x^2)
    6·1 answer
  • what should be done to both sides of the equation in order to solve 1/3 x = 4? multiply by 4, divide by 4, multiply by 1/3, divi
    15·1 answer
  • Find the standard deviation of the display of data.
    7·1 answer
  • Plz help I will give you 40 points and Brainly
    7·1 answer
  • True or False. 35 points!!<br><br> Vertical compressions make the parabola look skinnier.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!