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
irinina [24]
3 years ago
10

Show that the vector orthab=b-projacb is orthogonal to a.

Mathematics
1 answer:
Lina20 [59]3 years ago
3 0

Answer:

We have,  a. ortho (ab) = a.b - a.b/[a]² . /a/²

The /a/² cancel off each other, therefore,

a. ortho (ab) = a.b - a.b

a. ortho (ab) = 0

Therefore, the final result is 0.

Step-by-step explanation:

It should be noted that the orthogonal projection of a vector B onto A is given by a given formula known as:

proJ(ab)  = a.b/[a]² . a ............equation (1)

Where [a] is the magnitude of the vector a,

therefore, [a]² = a.a ...........equation (2)

Which means that if we have a dot product between a vector and the sum of vector, it can be distributed to each vector.

That is : a . (c - d + b )

a.b - a.d + a.b ...........................equation (3)

and since it is given that Ortho (ab) = b - proJ(ab)..........equation (4)

and in order to show that a two vector are orthogonal, we need to show that their dot product is zero.

Where : a.b = /a//b/ cos ( Ф)

and if the dot product is zero (0), this will imply that ,

cos (Ф) = 0

Now moving forward to the proof,,

The first thing we do is substitute equation (1) into equation (4)

That will give us : ortho (ab) =  b - a.b/[a]² . a

and in order to show that vector a and orth(ab) are orthogonal, we need to show that their dot is zero

Therefore, a . ortho (ab) = a . b -  a.b/[a]² . a ........equation (5)

Now, substituting equation (2) into (5),

We have,  a. ortho (ab) = a.b - a.b/[a]² . /a/²

The /a/² cancel off each other, therefore,

a. ortho (ab) = a.b - a.b

a. ortho (ab) = 0

Therefore, the final result is 0.

You might be interested in
100 POINTS PLUS BRAINLIST
vivado [14]
  • tanB=tanY
  • cosB=cosY
  • sinB=sinY

\\ \rm\hookrightarrow sinY=\dfrac{P}{H}=\dfrac{9.6}{29.6}=0.32

\\ \rm\hookrightarrow cosY=\dfrac{B}{H}=\dfrac{28}{29.6}=0.94

\\ \rm\hookrightarrow tanY=sinY/cosY=0.34

5 0
2 years ago
)) Fill in the missing number.<br> ()) 70% of<br> =<br> 56
Nutka1998 [239]

Answer: x=80

  • Step-by-step explanation: multiplying both sides by 100 and dividing both sides by 70  then we have x=56 x 100/70 then your answer is x=80. If you're using a calculator, simply enter 56x100 divided by 70  which will give you the answer  

6 0
2 years ago
The function F(x) is described below. F(x) = 3x + 2 What is the value of F(5)?
Musya8 [376]
f(x)=3x+2 \\  \\ f(5)=3*5+2=15+2=17
6 0
2 years ago
Please help me due today....
Monica [59]

Answer:

i belive it something with 4 and 6 like 10 or 4/6

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
ladessa [460]

Answer:

x is all real numbers

Step-by-step explanation:

The domain is the values for the inputs

Since all values are allowed for the input

The domain is all real numbers

8 0
3 years ago
Other questions:
  • A local restraunt offers you a deal if you purchase 3 medium pizzas you get 2 side dishes free if you get a total of 8 side dish
    7·1 answer
  • Find area A of the polygon with the given vertices A(-5,-2) B(4,-2) C(4,-7) D(-5,-7)
    5·1 answer
  • Expres 5m as a decimal of 12m, correct to three decimal places.
    15·2 answers
  • A researcher has collected the following sample data. The mean of the sample below is 5.
    6·1 answer
  • Solve: 2x+5x-11=-46<br><br>What is the value of x? <br>Please Help!!!
    13·1 answer
  • Which calculation be used to find the value of p in the equation p^3=8?​
    13·1 answer
  • Which of the following systems of linear equations has no solution?
    11·2 answers
  • a shopkeeper bought 2 watches for rs 400. he sold them to gain 5% one and loss 5% on other. calculate his final gain or loss per
    14·1 answer
  • 13 in<br> 4 in<br> On a cylinder
    8·1 answer
  • PLEASE HELP ME AND HURRY TOO NO LIBKS PLEASE I WILL GIVE BRAINLIEST
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!