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
Irina18 [472]
1 year ago
8

compute the projection of → a onto → b and the vector component of → a orthogonal to → b . give exact answers.

Mathematics
1 answer:
Nina [5.8K]1 year ago
3 0

\text { Saclar projection } \frac{1}{\sqrt{3}} \text { and Vector projection } \frac{1}{3}(\hat{i}+\hat{j}+\hat{k})

We have been given two vectors $\vec{a}$ and $\vec{b}$, we are to find out the scalar and vector projection of $\vec{b}$ onto $\vec{a}$

we have $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$

The scalar projection of$\vec{b}$onto $\vec{a}$means the magnitude of the resolved component of $\vec{b}$ the direction of $\vec{a}$ and is given by

The scalar projection of $\vec{b}$onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|}$

$$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\sqrt{1^2+1^1+1^2}} \\&=\frac{1^2-1^2+1^2}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{aligned}$$

The Vector projection of $\vec{b}$ onto $\vec{a}$ means the resolved component of $\vec{b}$ in the direction of $\vec{a}$ and is given by

The vector projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|^2} \cdot(\hat{i}+\hat{j}+\hat{k})$

$$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\left(\sqrt{1^2+1^1+1^2}\right)^2} \cdot(\hat{i}+\hat{j}+\hat{k}) \\&=\frac{1^2-1^2+1^2}{3} \cdot(\hat{i}+\hat{j}+\hat{k})=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\end{aligned}$$

To learn more about scalar and vector projection visit:brainly.com/question/21925479

#SPJ4

You might be interested in
Help me. And fasttttttttt.
ivann1987 [24]

Answer:

\sqrt{85} = 9.2195 = 9.22

\sqrt{17} = 4.123

Step-by-step explanation:

5 0
3 years ago
Debbie's city took a survey about a plan for a new park. The city surveyed 600 people. 60% of the people surveyed liked the plan
lukranit [14]
Hi there. 

All we have to do to find out how many people like the plan is multiplication.

We multiply the total number of people by 60% - in decimal form.

600 · 0.6 = 360

360 people liked the plan.
6 0
3 years ago
Read 2 more answers
Use the PACED decision-making process to _____.
Alex_Xolod [135]
Use the PACED decision-making process to make a decision or make a choice. The steps to follow when making a decision can be easily remembered when you use the word PACED:
P - What is the PROBLEM - Why is there a need to make a choice?
A - What are the ALTERNATIVES - What are the possible choices available?
C - Establish the CRITERIA - Why is one choice better than the other?
E - EVALUATE the alternatives - How well does each choice meet the criteria?
D - Make a DECISION - What is the best choice?
6 0
3 years ago
I need help because i’m not smart :)
8_murik_8 [283]
What is it referring too? is there a graph to it???
4 0
3 years ago
Read 2 more answers
Help me please help me
IceJOKER [234]

Answer:yes u do need help so go to a Psychiatric hospital

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • There are 45 rose bushes currently in the park. Park workers will plant more rose bushes today. When the workers are finished th
    14·2 answers
  • What is the vertex if the graph
    12·2 answers
  • What is the solution to the equation below? Round your answer to two<br> decimal places.<br> 2^3x=91
    5·2 answers
  • Please help, will mark!!
    5·1 answer
  • Solve the equation<br> 15x+2=45x+4
    15·1 answer
  • 34t-2=5-14t<br> solve for t PLEASE HELPPPPPP
    15·2 answers
  • Lines p and q are crossed by transversal s. Classify 1 and 5
    6·1 answer
  • What makes the equation true?<br><br> 5x(8+3) = 5x8 + __ x 3
    5·1 answer
  • Evaluate 5x for each value of x x = 0.3
    7·1 answer
  • Can anyone help me!​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!