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Vector A rightarrow has components Ax = 1.23cm , Ay = 2.45cm : vector B rightarr

ID: 1392566 • Letter: V

Question

Vector A rightarrow has components Ax = 1.23cm , Ay = 2.45cm : vector B rightarrow has components Bx = 4.05cm , By = -3.74cm . Find the components of the vector sum A rightarrow + B rightarrow . Express your answer as a comma-separated pair of components. Find the magnitude of the vector sum A rightarrow + B rightarrow . Find the counterclockwise angle the vector sum A rightarrow + B rightarrow makes with the +x axis. Please give your answer in the interval [0, 360] degree . Find the components of the vector difference B rightarrow - A rightarrow . Express your answer as a comma-separated pair of components. Find the magnitude of the vector difference B rightarrow - A rightarrow . Find the counterclockwise angle the vector difference B rightarrow - A rightarrow makes with the +x axis. Please give your answer in the interval [0, 360] degree .

Explanation / Answer

Part A:

let say resulatant component is

Rx=Ax+Bx

Rx=1.23 cm+4.05cm

Rx=5.28 cm

Ry=2.45-3.74

Ry=-1.29 cm

Rx=5.28 cm--Answer to A

Ry=-1.29 cm---Answer to A

Magnitute will be

R=sqrt(Rx^2+Ry^2)

R=sqrt(5.28^2+(-1.29)

R=sqrt(27.87+1.664)

B)R=5.43 cm

C) counter clockwise angle

And the angle is again from the right angled triangle:

tan^-1 (1.29 / 5.28)

=13.69 degrees in to clockwise direction

360-13.69=

346.31 degrees in anticlockwise direction---answer to C

D)

Component difference B-A

Rx=4.05-1.23

Rx=2.82 cm

Ry=-3.74-2.45

Ry=-6.19 cm

(2.82,-6.19) cm--answer to D

E) R=sqrt((2.82)^2+(-6.19)^2)

R=sqrt(7.95+38.3)

R=sqrt(46.26)

R=6.79 cm--answer to E

F)

And the angle is again from the right angled triangle:

tan^-1 (2.82 / 6.79)

=tan^-1(0.4153)

=22.51 degrees

360 - 22.51

= 337.49 degrees in an anticlockwise direction. answer to F