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
Norma-Jean [14]
3 years ago
10

Calculate the angle between (2,2,4) and (2,-1,1). The result is a familiar angle, so the answer is to be given exactly.

Mathematics
1 answer:
andrew-mc [135]3 years ago
6 0

Answer:

The angle between (2,2,4) and (2,-1,1) is 60º.

Step-by-step explanation:

From linear algebra, we can determine the angle between both vectors by definition of dot point:

\cos \theta = \frac{\vec u\bullet \vec v}{\|\vec u\|\cdot \| \vec v\|} (1)

Where:

\vec u, \vec v - Vectors.

\|\vec u\|, \|\vec v\| - Norms of vectors.

\theta - Angle between vectors, measured in sexagesimal degrees.

If we know that \vec u = (2,2,4) and \vec v = (2,-1,1), then angle between vectors is:

\|\vec u\| = \sqrt{\vec u\bullet \vec u} (2)

\|\vec u\| = \sqrt{2^{2}+2^{2}+4^{2}}

\|\vec u\| \approx 4.899

\|\vec v\| = \sqrt{\vec v\bullet \vec v} (3)

\|\vec v\| = \sqrt{2^{2}+(-1)^{2}+1^{2}}

\|\vec v\| \approx 2.450

\vec u \bullet \vec v = (2,2,4)\bullet (2,-1,1)

\vec u \bullet \vec v = 4-2+4

\vec u \bullet \vec v = 6

\cos \theta = \frac{6}{(4.899)\cdot (2.450)}

\cos \theta = 0.5

\theta = 60^{\circ}

The angle between (2,2,4) and (2,-1,1) is 60º.

You might be interested in
.......... ......................
MrRa [10]

Answer:

what do you need help on?

6 0
3 years ago
How do I factor this
melamori03 [73]
There is a factor of 10p in each term that is common, and thus, you can take them out of each term to yield 10p(p² - 196).
Now, 196 is a perfect square. That is, there is a real number that when multiplied by itself gives 196 (14).
Since p² - 14² is a difference of two squares, we can rewrite it as (p + 14)(p - 14).

So, our factored form is 10p(p + 14)(p - 14)
3 0
3 years ago
Which number is equal to 10^3
eduard

Answer: is 0.001

10^-3 = (1)/(10^3) move the negative exponent to the denominator (1)/(1000) simplify 10^3 in the denominator (1)/(1000) = 0.001

Step-by-step explanation:

Hope you have a great night

8 0
3 years ago
Hellllllllllllllppppppppppppppppppppppppppppp
strojnjashka [21]

Answer:

c

Step-by-step explanation:

30/5=6 4*6= 24

6 0
3 years ago
How many grams is 1.7kilograms​
belka [17]

Answer:

1700 grams...

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • How to multiply exponents with different bases and different exponents in exponential form?
    6·1 answer
  • “which expression is the factored form of x^2-7x+10?”
    15·1 answer
  • Question 30 please!!
    12·1 answer
  • Write a question about the<br> data in the chart. Then write<br> the answer to your question.
    5·1 answer
  • The Garcias have​ $12,000 in a saving account. The bank pays​ 3.5% interest on saving​ accounts, compounded monthly. Find the ba
    9·1 answer
  • Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y=x^2+x+9 a. D: al
    15·2 answers
  • BRAINLIEST!! 20 POINTS
    7·1 answer
  • Which scale factors results in an enlargement of an image along an opposite ray?
    15·1 answer
  • Which statement is true about the numbers marked on this horizontal number line?
    5·1 answer
  • Find the value of 7C7
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!