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2 years ago

What is 2/3 ÷ 4/52/3 5/61 1/53 1/3

Mathematics

1 answer:

steposvetlana [31]2 years ago

6 0

Answer:

5/6

Step-by-step explanation:

mental math

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

Nina [5.8K]

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

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

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1 year ago

Multiple to list the next five multiples of 3

brilliants [131]

Answer:

6, 9, 12, 15, 18

Step-by-step explanation:

Finding multiples is simple, count by 3 for as many times as you can and there are your multiples.

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2 years ago

john had a ribbon that was 1 1/2 meters long. he used 2 pieces that were each 1/3 of that length. how much ribbon did john use

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Of means multiplication. So the question is 1/3 X 1 1/2. First make 1 1/2 improper: 3/2. Then multiply the numerators (top numbers) and denominaters (bottom numbers): 1x3=3, 3x2=6, =3/6. Now simplify 3/6=1/2. Then multiply that by 2, since he used 2 pieces: 1/2x2=1. John used 1 meter :)

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2 years ago

What is 2/3 ÷ 4/52/3 5/61 1/53 1/3​

What is 2/3 ÷ 4/52/3 5/61 1/53 1/3