# Math Help - vectors again

1. ## vectors again

< is angle symbol

R is the resultant of the three forces A, B, and C, that is R = A+B+C If
A=A< 210, B= 100<20, C= 100<120, and R= R<195, use the component method to determine A and R.

ok so I broke them into components but have no idea how to find A and R..any help appreciated.

Ax= A cos 30= -?
Ay= A sin 30 = -?
Bx = 100 cos 20 = 93.9
By = 100 sin 20 = 34
Cx=100 sin 30= -50
Cy=100 cos 30= 86.6
Rx = R sin 15
Ry= R cos 15

where to begin...

2. Originally Posted by ur5pointos2slo
< is angle symbol

R is the resultant of the three forces A, B, and C, that is R = A+B+C If
A=A< 210, B= 100<20, C= 100<120, and R= R<195, use the component method to determine A and R.
$A\cos(210) + 100\cos(20) + 100\cos(120) = R\cos(195)$

$R = \frac{A\cos(210) + 100\cos(20) + 100\cos(120)}{\cos(195)}$

$A\sin(210) + 100\sin(20) + 100\sin(120) = R\sin(195)$

$R = \frac{A\sin(210) + 100\sin(20) + 100\sin(120)}{\sin(195)}$

set the two expressions equal to $R$ equal to each other and solve for $A$ ... then find $R$.

3. Originally Posted by skeeter
$A\cos(210) + 100\cos(20) + 100\cos(120) = R\cos(195)$

$R = \frac{A\cos(210) + 100\cos(20) + 100\cos(120)}{\cos(195)}$

$A\sin(210) + 100\sin(20) + 100\sin(120) = R\sin(195)$

$R = \frac{A\sin(210) + 100\sin(20) + 100\sin(120)}{\sin(195)}$

set the two expressions equal to $R$ equal to each other and solve for $A$ ... then find $R$.
The solution always seems obvious after someone else does it. Thank you for your help again.

4. Originally Posted by ur5pointos2slo
< is angle symbol

R is the resultant of the three forces A, B, and C, that is R = A+B+C If
A=A< 210, B= 100<20, C= 100<120, and R= R<195, use the component method to determine A and R.

ok so I broke them into components but have no idea how to find A and R..any help appreciated.

Ax= A cos 30= -?
Ay= A sin 30 = -?
Bx = 100 cos 20 = 93.9
By = 100 sin 20 = 34
Cx=100 sin 30= -50
Cy=100 cos 30= 86.6
Rx = R sin 15
Ry= R cos 15

where to begin...

I do not like the reduction of angles,
it is much too easy to lose the correct sign.

Ax = A cos(210) ; Ay = A sin(210)
Bx = 100 cos(020) ; By = 100 sin(020)
Cx = 100 cos(120) ; Cy = 100 sin(120)
======================================
Rx = R cos(195) ; Ry = R sin(195)

2 equations, 2 unknowns

-0.866 A + 93.969 -50.000 = -0.966 R
&
-0.500 A + 34.202 + 86.602 = -0.259 R

reduced:
-0.866 A + 43.969 = -0.966 R
-0.500 A + 120.804 = -0.259 R
&
-0.259(-0.866 A + 43.969) = -0.966(-0.500 A + 120.804 )
1 equation 1 unknown

(my response was toooo slow, need more coffee)

5. Originally Posted by aidan
I do not like the reduction of angles,
it is much too easy to lose the correct sign.

Ax = A cos(210) ; Ay = A sin(210)
Bx = 100 cos(020) ; By = 100 sin(020)
Cx = 100 cos(120) ; Cy = 100 sin(120)
======================================
Rx = R cos(195) ; Ry = R sin(195)

2 equations, 2 unknowns

-0.866 A + 93.969 -50.000 = -0.966 R
&
-0.500 A + 34.202 + 86.602 = -0.259 R

reduced:
-0.866 A + 43.969 = -0.966 R
-0.500 A + 120.804 = -0.259 R
&
-0.259(-0.866 A + 43.969) = -0.966(-0.500 A + 120.804 )
1 equation 1 unknown

(my response was toooo slow, need more coffee)
Thanks for your response though. They both were useful to me.

6. Originally Posted by aidan
I do not like the reduction of angles,
it is much too easy to lose the correct sign.

Ax = A cos(210) ; Ay = A sin(210)
Bx = 100 cos(020) ; By = 100 sin(020)
Cx = 100 cos(120) ; Cy = 100 sin(120)
======================================
Rx = R cos(195) ; Ry = R sin(195)

2 equations, 2 unknowns

-0.866 A + 93.969 -50.000 = -0.966 R
&
-0.500 A + 34.202 + 86.602 = -0.259 R

reduced:
-0.866 A + 43.969 = -0.966 R
-0.500 A + 120.804 = -0.259 R
&
-0.259(-0.866 A + 43.969) = -0.966(-0.500 A + 120.804 )
1 equation 1 unknown

(my response was toooo slow, need more coffee)
I do however think these are mixed up
-0.866 A + 93.969 -50.000 = -0.966 R
&
-0.500 A + 34.202 + 86.602 = -0.259 R

shouldnt it be

-0.866 A + 93.969 -50.000 = -0.259 R
&
-0.500 A + 34.202 + 86.602 = -0.966 R

or am i missing something

7. I got A=15.8 but compared to the rest of the values in the problem this seems very small. Could someone please verify if this is the correct value for A.