Answer
General guidance
Initially, find the horizontal and the vertical component of the force vector 
and represent it in vector form. Then, find the horizontal and the vertical component of the force vector 
and represent it in vector form.
Later, add both the forces in the vector form. Add the horizontal components of both the force vectors together and the vertical components of both the force vector together.
Finally, calculate the magnitude and the angle of the resultant force using the horizontal and the vertical components of the force.
A vector F can be represented as:
Here, 
is the x-component of the force, 
is the y-component of the force, 
and 
are the unit vectors which show the direction of the force in the x-axis and the y-axis respectively.
The expression for the magnitude of the resultant force is,
Here, is the x-component of the force and is the y-component of the force.
The expression of the direction of the resultant force is,
Here, 
is the angle between the x-component of the force 
and the y-component of the force 
.
Step-by-step
Step 1 of 4
(a)
Refer the figure given in the question.
The horizontal and the vertical components of the force vector is,
Here, 
is the horizontal component of the force 
, 
is the vertical component of the force 
, 
is the angle of the force making with the positive y-axis.
Substitute 250 lb for and 
for 
.
The vector form of the force 
is,
Substitute 
for 
and 
for 
.
The horizontal component of the force vector is in positive x-direction. The vertical component of the force vector is in positive y-direction.
Step 2 of 4
Refer the figure given in the question.
The horizontal and the vertical components of the force vector 
is,
Here, 
is the horizontal component of the force 
, 
is the vertical component of the force 
, 
is the angle of the force 
making with the positive x-axis.
Substitute 375 lb for 
and 
for 
.
The vector form of the force 
is,
Substitute 
for 
and 
for 
.
The horizontal component of the force vector 
is in positive x-direction. The vertical component of the force vector 
is in negative y-direction. The force is equal to the vector sum of the horizontal and the vertical component of the force .
is in positive y-direction is incorrect because the vertical component of the force vector 
is in negative y-direction.Step 3 of 4
The resultant force using the vector addition of the force and is,
Substitute 
for 
and 
for 
.
The expression for the magnitude of the resultant force is,
Substitute 
for 
and 
for 
.
The magnitude of the resultant force is 393 lb.
The resultant force can be calculated by the vector addition of the forces and . The resultant vector is the sum of the two vectors. The expression for the resultant vector is,
Here, 
are the two vectors.
is incorrect because the correct expression of the resultant force is Step 4 of 4
(b)
The expression of the direction of the resultant force 
is,
Substitute for and for .
The angle 
measured in counterclockwise direction from the x-axis is,
Substitute 
for 
.
The direction of the resultant force is 
.
The direction of the resultant force can be calculated using the horizontal component and the vertical component of the resultant force. The angle 
is 
measured in the clockwise direction from the positive x-axis. To measure the angle in the counter-clockwise direction, the angle is subtracted from 
to measure the angle in counterclockwise direction from the x-axis.
because the correct value of the vertical force is Answer
The magnitude of the resultant force is 393 lb.
The direction of the resultant force is .
Answer only
The magnitude of the resultant force is 393 lb.
The direction of the resultant force is .