Question

Find F1 + F2 - F3 from diagram

Answer 1

Given Forces

• F1=2N
• F2=2N
• F3=1N

Now lets find

$\\ \sf\longmapsto F_1+F_2-F_3$

• Put the values

$\\ \sf\longmapsto 2N+2N-1N$

$\\ \sf\longmapsto 4N-1N$

$\\ \sf\longmapsto 3N$

Answer 2

In these type of questions, we will totally use CONCEPTS OF VECTORS.

• First resolve the vectors in perpendicular components !

$F1 = 2 \hat{j}$

_____________

$F2= 2 \cos( {60}^{ \circ} ) \hat{i} - 2 \sin( {60}^{ \circ} ) \hat{j}$

$\implies F2= 1 \hat{i} - \sqrt{3} \hat{j}$

_____________

$F3= - 1 \cos( {30}^{ \circ} ) \hat{i} + 1\sin( {30}^{ \circ} ) \hat{j}$

$\implies F3= - \dfrac{ \sqrt{3} }{2} \hat{i} + \dfrac{1}{2} \hat{j}$

_____________

• Now, solve the questions:

$\vec{F1} + \vec{F2} - \vec{F3}$

$= (2 \hat{j}) + (\hat{i} - \sqrt{3} \hat{j}) - ( - \dfrac{ \sqrt{3} }{2} \hat{i} + \dfrac{1}{2} \hat{j})$

$\boxed{= \dfrac{2 + \sqrt{3} }{2} \hat{i} + \dfrac{3 - 2 \sqrt{3} }{2} \hat{j} }$

Hope It Helps.