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
Triss [41]
3 years ago
7

If a=i+7j+k and b=i+11j+k, find a unit vector with positive first coordinate orthogonal to both a and

Mathematics
1 answer:
Scilla [17]3 years ago
5 0
Take the cross product, then normalize the result.

\mathbf a\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\1&7&1\\1&11&1\end{vmatrix}=-4\,\mathbf i+4\,\mathbf k

This has norm

\|\mathbf a\times\mathbf b\|=\sqrt{(-4)^2+4^2}=4\sqrt2

and so a unit vector orthogonal to both given vectors is

\dfrac{\mathbf a\times\mathbf b}{\|\mathbf a\times\mathbf b\|}=-\dfrac1{\sqrt2}\,\mathbf i+\dfrac1{\sqrt2}\,\mathbf k

An equally correct answer would be the negative of this vector, since \mathbf b\times\mathbf a=-\mathbf a\times\mathbf b.
You might be interested in
1. Which diagram(s) show adjacent angles?
disa [49]

Answer:

1. diagrams C. D. and F. are adjacent angles, which are angles that share a vertex and side

2. diagram B. are vertical angles

3. diagram A. are complementary angles

4. diagram E. are supplementary angles

5. diagram D. is a linear pair

6 0
3 years ago
4. A video club costs $20 to join. Each video that is rented costs $2.25. Let v represent the number of videos.
shepuryov [24]

Answer:

B.

Step-by-step explanation:

$2.25 is the cost of each video that is rented, so $2.25 times v (or 2.25v) represents the cost of 'v' videos.

$20 is the constant, as it costs $20 to join the club. Since this doesn't change, it is the constant.

So, we would have the equation:

f(v) = 2.25v + 20

f(v) is the total cost.

B is your answer because it is the only one with the correct equation.

Hope this helps!

8 0
3 years ago
Simplify using i 3+2i/6+5i
alukav5142 [94]
The answer for your question question is 3+ 16/3 i
5 0
3 years ago
Determine the measure of each indicated angle. Show all necessary steps!
Rasek [7]

a)

We know that a 4-sided polygon's angles add up to 360 degrees

so to find x:

360-(69+118+84)=89 degrees

b)

For a 4-sided polygon we also know that the outside angles add up to 360 degree.

so to find p:

360-(100+62+106)=92 degrees

Hope it helps!

3 0
2 years ago
Estimate the square root to the nearest integer.
nexus9112 [7]
Answer:
3
Explanation:
3^2 is equal to 9, and 4^2 is equal to 16, so sqrt(10) must be in between 9 and 16. Since 10 is closer to 9 than to 16, sqrt(10) is closer to 3 than 4, which means that to the nearest integer sqrt(10)=3
3 0
3 years ago
Other questions:
  • Type the correct answer in each box.
    11·1 answer
  • Slope of (-3, 1) (3, -1)
    12·1 answer
  • How do I write 0.35 as money
    5·2 answers
  • How do I solve this?
    13·1 answer
  • Write an equation for the line that passes through the point (5, -4) and is parallel to the line y =
    6·1 answer
  • I need help on this question
    10·1 answer
  • A girl is on a train that is headed East at 100 miles per hour. The girl is walking at 5 miles per hour
    7·1 answer
  • A measurement that measures distance and it's basic unit is meter
    8·1 answer
  • Hwllppooppppoopppppppp
    14·2 answers
  • HELP ASAP !!! The table shows several points for function j(t).
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!