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
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