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  • A man starts from  <img alt="\vec{r_i}=2\hat{i}+4\hat{j}+6\hat{k}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cvec%7Br_i%7D%3D2%5Chat%7Bi%7D&plus;4%5Chat%7Bj%7D&plus;6

A man starts from  \vec{r_i}=2\hat{i}+4\hat{j}+6\hat{k} and moves velocity  \vec{v}=\vec{i}+4\hat{j}+5\hat{k} and its final position after 3 sec is.

Option: 1

16\hat{i}+5\hat{j}+21\hat{k}


Option: 2

5\hat{i}+16\hat{j}+21\hat{k}


Option: 3

5\hat{i}+21\hat{j}+16\hat{k}


Option: 4

4\hat{i}+7\hat{j}+13\hat{k}


Answers (1)

best_answer

The magnitude of position of vectors -

Magnitude: Its magnitude is the distance between the given point and its direction from the origin to that point.

\vec{r}= x\hat{i}+y\hat{j}+z\hat{k}

Magnitude : r= \sqrt{x^{2}+y^{2}+z^{2}}
 

 

r_i=2\hat{i}+4\hat{j}+6\hat{k}

 

\vec{r_f}=\vec{r_i}+\vec{v}t

=(2\hat{i}+4\hat{j}+6\hat{k})+(\hat{i}+4\hat{j}+5\hat{k})\times 3

=5\hat{i}+16\hat{j}+21\hat{k}

\left | \vec{r_f} \right |=\sqrt{5^2+16^2+21^2}=\sqrt{25+256+441}

=\sqrt{722}

Posted by

Gunjita

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