Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
0 votes

If a person standing at the point $(1,2) $ walks $5$ units towards east, then $3$ units towards north and $\sqrt 2$ units along the direction of $\hat i+\hat j$ and then walks $\sqrt 2 $ unit along the direction $\perp$ to this vector towards the starting point. What is the displacement of the person from origin?

(A) $(6+\sqrt 2)\hat i+(7+\sqrt 2)\hat j$

(B)$7\hat i+6\hat j$

(C) $6\hat i+7\hat j$

(D) $(7+\sqrt 2)\hat i+(6+\sqrt 2)\hat j$

Can you answer this question?

1 Answer

0 votes
Let the starting point be $A(1,2)\:\Rightarrow\:\overrightarrow {OA}=\hat i+2\hat j$
where $O$ is origin.
Then he moves 5 units towards east to $B$ (say) $\therefore \:\overrightarrow {OB}=6\hat i+2\hat j$
Then he moves 3 units north to $C$. $\therefore\:\overrightarrow {OC}=6\hat i+5\hat j$
Then he moves $\sqrt 2$ units towards the direction $\hat i+\hat j$ to $D$.
$\overrightarrow {CD}=\sqrt 2 (\large\frac{\hat i}{\sqrt 2}+\frac{\hat j}{\sqrt2})$$=\hat i+\hat j$
$\therefore\:$ In $\Delta OCD$, $\overrightarrow {OC}+\overrightarrow {CD}=\overrightarrow {OD}$
$\Rightarrow\:\overrightarrow {OD}=(6\hat i+5\hat j)+(\hat i+\hat j)=7\hat i+6\hat j$
Then he walks $\sqrt 2$ init $\perp$ to $\hat i+\hat j$ towards the starting point to $E$.
$\therefore\: $ the direction of $\overrightarrow {DE}$ is along $-\hat i+\hat j$
$\Rightarrow\:\overrightarrow {DE}=\sqrt 2(\large\frac{-\hat i}{\sqrt 2}+\frac{\hat j}{\sqrt 2})=-\hat i+\hat j$
$\therefore\:$ In $\Delta ODE$, $\overrightarrow {OD}+\overrightarrow {DE}=\overrightarrow {OE}$
$\therefore\:\overrightarrow {OE}=(7\hat i+6\hat j)+(-\hat i+\hat j)$
$=6\hat i+7\hat j$
answered Dec 10, 2013 by rvidyagovindarajan_1
edited Mar 13, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App