Vector v1 is 6.6 units long and points along the negative x axis. vector v2 is 8.5 units long and points at + 55° to the positive x axis. (a) what are the x and y components of each vector? (b) determine the sum v v 1 2

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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(a) what are the x and y components of each vector?
 For vector v1:
 v1 = 6.6 (cos (180) i + sine (180) j)
 v1 = 6.6 (-1i + 0j)
 v1 = -6.6i
 For vector v2:
 v2 = 8.5 (cos (55) i + sine (55) j)
 v2 = 8.5 ((0.573576436) i + (0.819152044) j)
 v2 = 4.88 i + 6.96 j
 (b) determine the sum v v 1 2

 The sum of both vectors is given by:
 v1 + v2 = (-6.6i) + (4.88 i + 6.96 j)
 Adding component to component:
 v1 + v2 = (-6.6 + 4.88) i + (6.96) j
 v1 + v2 = (-1.72) i + (6.96) j

The correct answer should be $702.53