You are given a vector in the xy plane that has a magnitude of 84.0 units and a y-component of -67.0 units.

(a) what are the two possibilities for its x-component?

(b) 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 negative x-direction.

(c) specify the direction of the vector.

Explanation:

a)Magnitude =

84=

x= +50.67 or -50.67 units

b) We are given that the resultant is entirely in the -ve x direction which means that the y-component of the resultant is 0; It means that the y-component of the next vector = -ve of the y component of the initial vector i.e 67.

To make the magnitude 80 units in the negative x direction where the y component is 0, the x component must be -130.67(-50.67 - 80) as the x component is + 50.67units.

Magnitude = = 146.85 units

c) The direction vector = 67/146.85 i  - 130.67/146.85 j where i corresponds to the vector in y direction and j corresponds to the vector in x direction. Or this vector is at an angle of 180 - i.e 152.85 degrees from the +ve x-axis.

12000j is work done