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Find the angle between force vec(F) =(3hat(i)+4hat(j)-5hat(k)) unit and displacement vec(d)=(5hat(i)+4hat(j)+3hat(k)) unit , Also find the projection of F on d .

Answer» <html><body><p></p>Solution :`<a href="https://interviewquestions.tuteehub.com/tag/vec-723433" style="font-weight:bold;" target="_blank" title="Click to know more about VEC">VEC</a>(F) =<a href="https://interviewquestions.tuteehub.com/tag/3hat-1863202" style="font-weight:bold;" target="_blank" title="Click to know more about 3HAT">3HAT</a>(i)+4hat(j)-5hat(k)` <br/> `vec(d) =5hat(i)+4hat(j)+3hat(k)` <br/> `vec(F).vec(d) =(3hat(i)+4hat(j)-5hat(k)).(5hat(i)+4hat(j)+3hat(k))`<br/> ` = <a href="https://interviewquestions.tuteehub.com/tag/15-274069" style="font-weight:bold;" target="_blank" title="Click to know more about 15">15</a>+16 - 15`<br/> = 16 unit<br/>` | vec(F) | = sqrt((3)^(2)+(4)^(2)+(-5)^(2))`<br/> `= sqrt(9+16+25)`<br/> ` =sqrt(50)` <br/> `|vec(F)| =sqrt((3)^(2)+(4)^(2)+(-5)^(2))`<br/> `=sqrt(25+16+9)` <br/> `= sqrt(50)` <br/> `|vec(d)|=sqrt((3)^(2)+(4)^(2)+(-5)^(2))` <br/> Now `vec(F).vec(d) =| vec(F) | |vec(d)| cos theta `<br/> ` :. cos theta= (vec(F).vec(d))/(|vec(F)||vec(d)|)` <br/> `= 16/((sqrt(15))(sqrt(50)))` <br/> ` =16/15` <br/> ` :. cos theta =0.32` <br/> `sin(90^(@) - theta) = 0.32 ` <br/> `90^(@) - theta =18^(@)40` <br/> ` :. theta = 90^(@) - 18^(@) 40` <br/> ` :.theta = 71^(@) <a href="https://interviewquestions.tuteehub.com/tag/21-293276" style="font-weight:bold;" target="_blank" title="Click to know more about 21">21</a> ` <br/> <a href="https://interviewquestions.tuteehub.com/tag/projection-1169328" style="font-weight:bold;" target="_blank" title="Click to know more about PROJECTION">PROJECTION</a> of F on d <br/>=`F cos theta ` <br/> ` = sqrt(50) xx0.32 ` <br/> ` = 2.263` N<br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C06_E02_001_S01.png" width="80%"/></body></html>


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