Respuesta :
Answer:
The angle will be "124°". The further explanation is given below.
Explanation:
As we know,
[tex]\vec{A}=2m\hat{i}+3m\hat{j}[/tex]
[tex]\vec{B}=4Cos65^{\circ}\hat{i}+4Sin65^{\circ}\hat{j}[/tex]
[tex]\vec{C}=-4m\hat{i}-6m\hat{j}[/tex]
[tex]\vec{D}=5Cos55^{\circ}\hat{-i}+5Sin55^{\circ}\hat{j}[/tex]
(a)...
Let the resultant of [tex]\vec{A}[/tex], [tex]\vec{B}[/tex], [tex]\vec{C}[/tex] and [tex]\vec{D}[/tex] will be [tex]\vec{R}[/tex], then
⇒ [tex]\vec{R}=\vec{A}+\vec{B}+\vec{C}+\vec{D}[/tex]
On putting values, we get
⇒ [tex]=(2+4Cos65^{\circ}-4+5Cos55^{\circ})\hat{i}+(3+4Sin65^{\circ}-6+5Sin55^{\circ})\hat{j}[/tex]
⇒ [tex]=3.17741m(\hat{i})+4.721m(\hat{j})[/tex]
(b)...
On squaring both sides, we get
⇒ [tex]\left |\vec{R} \right |=\sqrt{(3.17741)^{2}+(4.721)^{2}}[/tex]
⇒ [tex]=5.7 \ m[/tex]
(c)...
Let the resultant angle will be "[tex]\theta[/tex]",
⇒ [tex]tan(180-\theta)=\frac{4.721}{3.17741}[/tex]
⇒ [tex]180-\theta=56.06[/tex]
⇒ [tex]\theta=124^{\circ}[/tex]
