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topjm [15]
3 years ago
8

Find two unit vectors orthogonal to both 8, 5, 1 and −1, 1, 0 .

Mathematics
1 answer:
Elina [12.6K]3 years ago
7 0
In order to do this, you must first find the "cross product" of these vectors. To do that, we can use several methods. To simplify this first, I suggest you compute:

‹1, -1, 1› × ‹0, 1, 1›

You are interested in vectors orthogonal to the originals, which don't change when you scale them. Using 0,-1,1 is much easier than 6s and 7s.

So what methods are there to compute this? You can review them here (or presumably in your class notes or textbook):
http://en.wikipedia.org/wiki/Cross_produ...

In addition to these methods, sometimes I like to set up:
‹1, -1, 1› • ‹a, b, c› = 0
‹0, 1, 1› • ‹a, b, c› = 0

That is the dot product, and having these dot products equal zero guarantees orthogonality. You can convert that to:

a - b + c = 0
b + c = 0

This is two equations, three unknowns, so you can solve it with one free parameter:

b = -c
a = c - b = -2c

The computation, regardless of method, yields:
‹1, -1, 1› × ‹0, 1, 1› = ‹-2, -1, 1›

The above method, solving equations, works because you'd just plug in c=1 to obtain this solution. However, it is not a unit vector. There will always be two unit vectors (if you find one, then its negative will be the other of course). To find the unit vector, we need to find the magnitude of our vector:

|| ‹-2, -1, 1› || = √( (-2)² + (-1)² + (1)² ) = √( 4 + 1 + 1 ) = √6

Then we divide that vector by its magnitude to yield one solution:

‹ -2/√6 , -1/√6 , 1/√6 ›

And take the negative for the other:

‹ 2/√6 , 1/√6 , -1/√6 ›
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S = 1 / g t ² π, solve for t​
Finger [1]

s =   \frac{1}{g {t}^{2}\pi }

multiply through by

g {t}^{2} \pi

s \times g {t}^{2} \pi =  \frac{1}{g {t}^{2} \pi}  \times g {t}^{2} \pi

sg {t}^{2} \pi = 1

dividing through by

sgπ

{t}^{2}  =  \frac{1}{sg\pi}

t =  \sqrt{ \frac{1}{sg\pi} }

4 0
3 years ago
Read 2 more answers
22 POINTS
Harlamova29_29 [7]

Answer:

C. 2, -2, -6

Step-by-step explanation:

18, 14, 10, 6, ?

18 - 4 = 14

14 - 4 = 10

10 - 4 = 6

6 - 4 = 2

2 - 4 = -2

-2 - 4 = -6

They are subtracting each number by 4 to get the next one that continues.

Hope this helped!

Have a supercalifraglisticexpialidocious day!

7 0
2 years ago
Read 2 more answers
I really need help for this geometry question, I would appreciate any help thank you.
Vsevolod [243]
You know that you have the Opposite side and the Adjacent side. therefore you would use Tangent (T= O/A)
because you are finding the angle you would go Tan^-1(12÷20) =31°
it is 12÷20 because O/A and the 12 is the opposite side therefore It would be O and 20 is the adjacent side therefore equaling 20 so O/A = 12/20
Your answer is 31°
8 0
2 years ago
The median for the given set of six ordered values is 28.5
Alika [10]
X=the missing value

the median is the middle number, but in this case there are two which happens to be 25 and x
so the formula is

25+x/2=31.5
use algebra to solve
25+x=63
x=63-25
x= 38

Therefore, the missing value is 38.

Hope this helped. Let me know if you have any further questions:)
6 0
3 years ago
31. A business rents cars for $150 a day and vans for $300 a day. One day it rented a total of 30 vehicles and
Advocard [28]

Answer:

D. 22 Cars and 8 Vans

Step-by-step explanation:

1. You multiply 22 x 150 = 3,300.

2. Then you multiply 300 x 8 = 2,400.

3. Next, add 3,300 + 2,400

4. That equals 5700.

Hopefully, that helps!

7 0
3 years ago
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