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
Xelga [282]
3 years ago
13

Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Mathematics
1 answer:
Maurinko [17]3 years ago
6 0
The cross product of two vectors gives a third vector \mathbf v that is orthogonal to the first two.

\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k

Normalize this vector by dividing it by its norm:

\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)

To get another vector orthogonal to the first two, you can just change the sign and use -\mathbf v.
You might be interested in
3x^2+6x-9=0 complete the square
PolarNik [594]
You could simplify this work by factoring "3" out of all four terms, as follows:

3(x^2 + 2x - 3) =3(0) = 0

Hold the 3 for later re-insertion.  Focus on "completing the square" of x^2 + 2x - 3.

1.  Take the coefficient (2) of x and halve it:  2 divided by 2 is 1
2.   Square this result:  1^2 = 1
3.   Add this result (1) to x^2 + 2x, holding the "-3" for later:
                    x^2 +2x 
4    Subtract (1) from x^2 + 2x + 1:     x^2 + 2x + 1               -3 -1  =    0, 
       or      x^2 + 2x + 1 - 4 = 0
5.   Simplify, remembering that x^2 + 2x + 1 is a perfect square:

                        (x+1)^2 - 4 = 0

We have "completed the square."  We can stop here.  or, we could solve for x:  one way would be to factor the left side:

            [(x+1)-2][(x+1)+2]=0     The solutions would then be:

             x+1-2=0=> x-1=0, or x=1, and
             x+1 +2 = 0 => x+3=0, or x=-3.  (you were not asked to do this).


3 0
2 years ago
Janie has \$3$3dollar sign, 3. She earns \$1.20$1.20dollar sign, 1, point, 20 for each chore she does and can do fractions of ch
madreJ [45]

Answer:

9

Step-by-step explanation:

13.50 - 3 = 10.50

1.20×8 = 9.60 = not enough

1.20×9= 10.80 = more than enough

She has to do 9 chores to have enough money including the 3 dollar she already has

8 0
2 years ago
Read 2 more answers
How many sentences are in 3 paragraph.
masya89 [10]
There is 15 sentence in 3 paragraph
6 0
3 years ago
Read 2 more answers
Samuel solved the equation h-234=1,192 and found the solution to be h=958. Is he correct? If not, why not?
Naya [18.7K]

Answer:

no he is not correct because he did not add 234 and 1192 to find the value of h, which is 1426


Step-by-step explanation:

h-234 = 1192

add 234 to each side

h-234+234= 1192+234

h = 1192+234

h = 1426


4 0
3 years ago
Read 2 more answers
Need help on this math question
8090 [49]

= 2^-16 * 3^10 * 3^-8 * 3^-12 * 2^28

= 2^(-16 + 28) * 3^(10 - 8 - 12)

= 2^12 * 3^-10

= 2^12 / 3^10

7 0
3 years ago
Other questions:
  • Amy cut 32 ft of chain into pieces that were each ft long. How many of these did Amy have after cutting the chain?
    15·1 answer
  • If the beginning balance of the Accumulated Depreciation—Equipment account is $10,000 and an adjusting journal entry for depreci
    10·2 answers
  • Write the difference as a sum.<br> -15 - (-7)
    6·2 answers
  • Consider the diagram below.<br> Which of the following statements is correct?
    5·2 answers
  • If you have to drive 200 miles and someone drives 4/10 of the distance and some one else drives 20% what does the other person.
    9·1 answer
  • Please help I beg you, I will pay too
    15·1 answer
  • I FREAKING NEED HELPPP!!!
    13·1 answer
  • On a certain map, 1.2 represents 12 miles. Lenoir City and Greenback are 6 inches apart on the map. What is the actual distance
    13·2 answers
  • Find the value of x help pls
    9·1 answer
  • Algebra 1 ,pls answer and tell me as fast as you can
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!