The rectangular components of a vector can be found out by the following formulae
The x component = Fx= F Cosθ
The y component= Fy = F Sine θ
The vector V1 has
Fx= -6.6 units
Fy= 0 units
The vector V2 has
Fx= 4.875 units
Fy= 6.963 units
The resultant vector obtained by the sum of two vectors is V= 1.9 units along the positive x- axis.
Putting the values in the above formulae we can find the x and y components.
For vector 1
The vector V1 is 6.6 units and makes an angle of 180°
Fx= F Cosθ = 6.6 Cos 180°= 6.6×-1 = -6.6
Fy= F Sine θ= 6.6 Sine 180°= 6.6× 0 = 0
Fx= -6.6 shows that the rectangular component along the x axis is in the opposite direction or the negative x-axis.
Fy= 0 shows that the rectangular component along the y axis of the given vector does not exist as the magnitude is zero .
For vector 2
The vector V2 is 8.5 units and makes an angle of 55°
Fx= F Cosθ = 8.5 Cos 55°= 8.5× 0.574= 4.875
Fy= F Sine θ= 8.5 Sine 55°= 8.5× 0.819 = 6.963
Fx= 4.875 shows that the rectangular component along the x axis has a magnitude of 4.875 and is along the positive x-axis.
Fy= 6.963 shows that the rectangular component along the y axis has a magnitude of 6.963 and is along the positive y- axis.
The sum of the two vectors can be obtained if they are drawn in the same direction .
As the first vector V1 is in the opposite direction to the second vector then this vector can be subtracted from the second vector V2.
Resultant Vector= V= V1+ V2
= -6.6+ 8.5
= 1.9
The resultant vector V= 1.9 units along the positive x- axis.
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