Question

You are given a vector in the xy plane that has a magnitude of 81.0 units and a y component of -57.0 units.

What are the two possibilities for its x component?

Enter your answers using three significant figures separated by a comma.

x1, x2 =

57.5,-57.5

units

Assuming the x component is known to be positive, specify the magnitude of the vector which, if you add it to the original one, would give a resultant vector that is 80.0 units long and points entirely in the −x direction.

V =

149

units

Question

Specify the direction of the vector.

Express your answer using three significant figures.

Answer 1

the two possiblities for it's x component

as the magnitude of 81 units

hence , the possible values are (81 , -81 ) unit

Now, if the x component is positive

our vector will be

a = 81 i - 57 j

Now , for the resultant to be - 80 i

a + b = - 80 i

81 i - 57 j + b = - 80 i

b = -161 i + 57 j

Now, for the magnitude of vector

magnitude of vector = sqrt(161^2 + 57^2)

magnitude of vector = 170.8 units

direction of vector = 180 - atan(57/161)

direction of vector = 160 degree

the direction of vector is 160 degree with + x axis