Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  TN XII Math  >>  Vector Algebra
0 votes

A force magnitude $5$ units acting parallel to $\overrightarrow{2i}-\overrightarrow{2j}+ \overrightarrow{k}$ displaces the point of application from $(1,2,3)$to $(5,3,7) $ find the work done.

Can you answer this question?

1 Answer

0 votes
  • The work done by a force $ \overrightarrow F$ in displacing a particle through $ \overrightarrow d$ is $ \overrightarrow F.\overrightarrow d = |\overrightarrow F| $ ( displacement in the direction of $ \overrightarrow F$)
  • The unit vector in the direction of $ \overrightarrow a$ is given by $ \overrightarrow a = \large\frac{\overrightarrow a}{|\overrightarrow a|}$
The particle is displaced from $ A(1,2,3) [ \overrightarrow {OA} = \overrightarrow i+2 \overrightarrow j+3 \overrightarrow k]$ to $B(5,3,7) [ \overrightarrow {OB}=5 \overrightarrow i+3 \overrightarrow j+7 \overrightarrow k]$
The displacement is $ \overrightarrow d = \overrightarrow {OB}- \overrightarrow {OA} = 4 \overrightarrow i+ \overrightarrow j+4 \overrightarrow k$
$ \overrightarrow F=5 \overrightarrow a$ where $ \overrightarrow a$ is the unit vector in the direction $ \overrightarrow a=2 \overrightarrow i-2 \overrightarrow j+ \overrightarrow k.\: | \overrightarrow a| = \sqrt{4+4+1}=3$
$ \therefore \overrightarrow a = \large\frac{1}{3}$$ ( 2 \overrightarrow i-2 \overrightarrow j+ \overrightarrow k) \: and \: \overrightarrow F = \large\frac{5}{3}$$ ( 2 \overrightarrow i-2 \overrightarrow j+ \overrightarrow k)$
$ \therefore $ work done $ w = \overrightarrow f. \overrightarrow d=\large\frac{5}{3}$$ (2 \overrightarrow i-2 \overrightarrow j+ \overrightarrow k).(4 \overrightarrow i+ \overrightarrow j+4 \overrightarrow k)$
$ = \large\frac{5}{3} $$( (2)(4)+(-2)(1)+(1)(4))$
$ = \large\frac{5}{3}$$ [ 8-2+4]= \large\frac{50}{3}$ units
answered Jun 4, 2013 by thanvigandhi_1
edited Jul 18, 2013 by balaji.thirumalai

Related questions

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