Physics vector problem please help?

how do i solve this?


i can get it start it but i cant complete it





Vector A,B and C are given.


Vector A has x-component = +3.00 and y-component=+4.00


vector B has x-component = +5.00 and y -component =-7.00


vector c has x-component = -2.00 and y -component= +1.00





find the resultant vector R





thank you

Physics vector problem please help?
A = %26lt;+3.00, +4.00%26gt;


B = %26lt;+5.00, -7.00%26gt;


C = %26lt;-2.00, +1.00%26gt;





A + B + C = %26lt;+3.00 +5.00 -2.00, +4.00 -7.00 +1.00%26gt;





A + B + C = %26lt;+6.00, -2.00%26gt;





%26lt;x, y%26gt; = %26lt;+6.00, -2.00%26gt; (rectangular)





x = r cos (theta)


y = r sin (theta)


x^2 + y^2 = r^2


tan(theta) = (y/x)





%26lt;r, theta%26gt; = %26lt;6.32, 0.3218%26gt; (polar--theta in radians)
Reply:A = 3i + 4j


B = 5i - 7j


C = -2i + j


Resultant R = A + B + C


= (3i + 4j) + (5i - 7j) + (-2i + j)


= 6i - 2j


Magnitude of resultant = √[(6)^2 + (-2)^2] = 2√(10)


Unit vector in the direction of the resultant


= [1/2√(10)] (6i - 2j) = cos θ i + sin θ j


=%26gt; cos θ = 3/√(10) and sin θ = - 1/√(10)


where, θ is the angle with the positive direction of x-axis and is in the fourth quadrant.
Reply:The magnitude of each vector is given by (mag^2 |x| + mag^2 |y|)^(1/2).





So vector A has magnitude (3^2 + 4^2)^(1/2) = 5. It has resultant direction tan(x) = 3/4. Vector A = (36.9 degrees, 5).





Vector B has magnitude sqrt(74), and resultant direction tan(x) = -7/5. Vector B = (-54.5 degrees, sqrt(74)).





Vector C has magnitude sqrt(5). tan(x) = -2/1. x = -63.4. Vector C = (-63.4 degrees, sqrt(5)).





Hope this helps.