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
Please help giving all my points
Kay [80]

Answer:

Step-by-step explanation:

1. Subtraction

2.multiplication

6 0
3 years ago
Read 2 more answers
The radius of a circle is 5m, what is the diameter​
Artyom0805 [142]

Answer:

10

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Slove for P. 5/7=p+4/7
Sever21 [200]
p= 1/7
Alright, so first, you need to flip the equation.<span><span>It will turn into p+<span>4/7</span></span>=<span>5/7
Next, you want to get the variable by itself so you need to subtract 4/7 from both sides. 5/7-4/7=1/7
p=1/7</span></span>
5 0
3 years ago
(14+42-6)/10+7^2 order of operation
Rainbow [258]

Answer:

54

Step-by-step explanation:

\dfrac{(14+42-6)}{10}+7^2

Parentheses (14 + 42 - 6) = 50:

⇒ 50/10 + 7²

Exponents 7² = 49:

⇒ 50/10 + 49

Multiplication/division  50/10 = 5:

⇒ 5 + 49

Addition/subtraction:  5 + 49 = 54

⇒ 54

6 0
3 years ago
Find the greatest common factor of each set of numbers 12 54
max2010maxim [7]
I hope this helps you

4 0
3 years ago
Other questions:
  • Find the angles between -pi and pi that satisfy:<br><br> (−√3) sin(v)+cos(v)=√3
    9·1 answer
  • My favorite songstress gives away 25% of the sales of her signature fragrance collection to her charity. Last month her sales we
    7·1 answer
  • the function f(x) = 3,005(1+0.03)^x represents the amount of money in a savings account where x represents time in years. what d
    14·2 answers
  • Enter the measurement with the indicated number of significant digits.
    11·1 answer
  • Which model represents 0.69 divided by 3 I need this ASAP DUE IN 5 minutes
    12·1 answer
  • Identify THREE vocabulary words that also refer to x-intercepts.
    14·2 answers
  • In ΔTUV, t = 560 inches, v = 400 inches and ∠V=19°. Find all possible values of ∠T, to the nearest degree
    9·1 answer
  • a can do.a piece of work in 6 days and B in 8 days each working 7hours a day In what time will they finish it together, working
    14·1 answer
  • 90000 1000 + 7000 + 7 =​
    9·2 answers
  • Help me pleaseeeeeeeee​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!