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
Stolb23 [73]
3 years ago
6

The angle θ between 5i-j+k & 2i-j+k is​

Mathematics
1 answer:
Maksim231197 [3]3 years ago
7 0

Step-by-step explanation:

Let,

\sf \vec{a} = 5 \hat{i} -  \hat{j}  +  \hat{k} \\  \therefore \: \sf \:   | \vec{a}|  =  \sqrt{ {5}^{2}  +  {( - 1)}^{2}  +  {1}^{2} }  \\  =  \sqrt{25 + 1 + 1}  \\  =  \sqrt{27}  \\  \\  \sf \vec{b} = 2\hat{i} -  \hat{j}  +  \hat{k} \\ \therefore \: \sf \:  | \vec{b}|  =  \sqrt{ {2}^{2}  +  {( - 1)}^{2}  +  {1}^{2} }  \\  =  \sqrt{4 + 1 + 1}  \\  =  \sqrt{6}  \\  \\\sf \: \vec{a}. \vec{b} = (5 \hat{i} -  \hat{j}  +  \hat{k}).(2\hat{i} -  \hat{j}  +  \hat{k}) \\  = 5 \times 2 + ( - 1) \times ( - 1) + 1 \times 1 \\  = 10 + 1 + 1 \\  = 12 \\  \\  \sf \: angle \: between \:  \vec{a} \: and \:  \vec{b} \:  = \theta \\  \\  \: so \\  \sf \vec{a}. \vec{b} =  | \vec{a}| . | \vec{b}| cos\theta \\  =  > \sf \:  cos \theta \:  =  \frac{ \vec{a}. \vec{b}}{ | \vec{a}| . | \vec{b}| }  \\  =  > cos \theta =  \frac{12}{ \sqrt{27}  \times  \sqrt{6}  }  = 0.94 \\  =  >  \theta =  {cos}^{ - 1} (0.94) \\  =  >   \green{\theta = 19.47 ^{ \circ} }

You might be interested in
A hand-held digital music player was marked down by 1/4 of the original price. If the sales price is $200. What is the original
Xelga [282]

Answer:A boo

Step-by-step explanation: trust me :) ✨

5 0
2 years ago
One number exceeds another by 1. the sum of the numbers is 21. what are the numbers
Cerrena [4.2K]
Try this solution:
1. if 1st number is 'x', the 2d number is 'y', then it is possible to make up the system of two equation according to the condition:
\left \{ {{x-y=1} \atop {x+y=21}} \right. \ =\ \textgreater \  \  \left \{ {{x=11} \atop {y=10}} \right.
2. one number is 11, another number is 10.
3 0
3 years ago
The line plot below shows the weight of each of 15 ostrich eggs . What is the total weight of the 3 heaviest eggs
erica [24]

Answer:

D). 6 3/4

Step-by-step explanation:

Given,

The three eggs with the heaviest weights are;

2\frac{1}{2} ounces

2\frac{1}{4} ounces, &

2 ounces

To find,

The total weight of the three heaviest eggs = 2\frac{1}{2} ounces + 2\frac{1}{4} ounces + 2 ounces

= 5/2 + 9/4 + 2/1

Taking the L.C.M. of 2, 4, and 1,

= 10/4 + 9/4 + 8/4

= (10 + 9 + 8)/4

= 27/4 or 6 3/4

4 0
3 years ago
Number 3. What is the value of x?
kodGreya [7K]

Answer:

the value of x would be 7

Step-by-step explanation:

because im smartttt

7 0
3 years ago
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is
vampirchik [111]

we know that A has 60% of salt, so if way we had "x" amount of ounces of A solution the amount in it will be 60% of "x", or namely (60/100)*x = 0.6x.

Likewise for solution B if we had "y" ounces of it, the amount of salt in it will be (75/100) * y or 0.75y, thus

\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of }}{amount}\\ \cline{2-4}&\\ A&x&0.60&0.6x\\ B&y&0.75&0.75y\\ \cline{2-4}&\\ mixture&60&0.65&39 \end{array}~\hfill \begin{cases} x+y=60\\ 0.6x+0.75y=39 \end{cases} \\\\\\ \stackrel{\textit{since we know that}}{x+y=60}\implies y = 60 - x~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.6x+0.75(60-x)=39}

0.6x+45-0.75x=39\implies -0.15x+45=39\implies -0.15x=-6 \\\\\\ x = \cfrac{-6}{-0.15}\implies \boxed{x = 40} \\\\\\ \stackrel{\textit{we know that}}{y = 60 - x}\implies y = 60-40\implies \boxed{y = 20}

3 0
2 years ago
Other questions:
  • Find the commission on a $590.00 sale if the commission is 15%.
    9·2 answers
  • If r = x, y, z and r0 = x0, y0, z0 , describe the set of all points (x, y, z) such that |r − r0| = 5.
    10·2 answers
  • Solve the system using multiplication for the linear combination method.
    6·2 answers
  • A cone and a cylinder have the same size base. The cones height is 6 times the height of the cylinder. How much greater is the v
    7·1 answer
  • What number completes this number
    8·1 answer
  • Triangle ABC is similar to triangle DEF. If angle A measures 28 degrees and angle B measures 74 degrees. If angle F is the large
    14·2 answers
  • Anna and Liam time travel the country selling handmade leather bracelets at the state fair. Before traveling to Newtown, they bu
    10·1 answer
  • HURRY , Write the coordinates of the vertices after a reflection across the line x = 5. (will give brainiest)
    12·1 answer
  • I dont get it ? And need an explanation yk
    14·1 answer
  • Graph the equation
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!