Thread: isolate terms in vector equation?

A traffic light weighing 22 lbs is hanging from a cable on the right at 60 degrees (force vector T1) and a cable on the left at 45 degrees (force vector T2). From this we get the vector equation:
-T2(cos45i) + T1(cos30i) + T2(sin45j) + T1(sin30j) -22j = 0
Can you tell me how to isolate the T1 and T2 force vectors and solve the equation, please?

Originally Posted by sifaka

A traffic light weighing 22 lbs is hanging from a cable on the right at 60 degrees (force vector T1) and a cable on the left at 45 degrees (force vector T2). From this we get the vector equation:
-T2(cos45i) + T1(cos30i) + T2(sin45j) + T1(sin30j) -22j = 0
Can you tell me how to isolate the T1 and T2 force vectors and solve the equation, please?

You separate i and j components first: -T2 cos(45)+ T1 cos(30)= 0 and T2sin(45)+ T1cos(30)- 22= 0 or T2sin(45)= T1cos(30)= 22. You now have two equations in two unknown variables. One way to solve would be to multiply the first equation by sin(45) and the second equation by cos(45). That makes the coefficient of T2 in the first equation -sin(45)cos(45) and in the second equation sin(45)cos(45). Adding the two equations, those cancel leaving an equation in T1 only.

By the way, you know that , cos(60)= 1/2 and , don't you?