**Q1: **

Two parallel forces have magnitudes of 21 N and 27 N. The distance between their lines of action is 20 cm. If the two forces are acting in the same direction, find their resultant and the distance between its line of action and point .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q2: **

Two parallel forces have magnitudes of 10 N and 20 N. The distance between their lines of action is 30 cm. If the two forces are acting in the same direction, find their resultant and the distance between its line of action and point .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q3: **

Given that , where , and their resultant is acting at a point that is 16 cm away from , determine the distance between the resultant’s line of action and .

**Q4: **

Given that , where , and their resultant is acting at a point that is 24 cm away from , determine the distance between the resultant’s line of action and .

**Q5: **

The figure below shows the two parallel forces 48 N and 32 N and their resultant . If , determine and the length of .

- A ,
- B ,
- C ,
- D ,

**Q6: **

The figure below shows the two parallel forces 30 N and 12 N and their resultant . If , determine and the length of .

- A ,
- B ,
- C ,
- D ,

**Q7: **

The figure below shows the two parallel forces 27 N and 9 N and their resultant . If , determine and the length of .

- A ,
- B ,
- C ,
- D ,

**Q8: **

The figure below shows the two parallel forces 45 N and 30 N and their resultant . If , determine and the length of .

- A ,
- B ,
- C ,
- D ,

**Q9: **

and 12 N are two parallel forces, where is their resultant. Given that and , determine the magnitudes of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q10: **

Two vertical forces are acting on a horizontal light rod . The smaller force has magnitude 60 N and acts on end . The other force acts on end . Determine the length of the rod given that the magnitude of the forces’ resultant equals 94 N, and the distance between its line of action and is 24 cm.

**Q11: **

Two parallel forces and have the same direction, and the distance between their lines of action is 90 cm. Given that the magnitude of their resultant is 49 N, and it is 60 cm away from , find the magnitudes of the two forces, rounding your answer to two decimal places if necessary.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q12: **

Two parallel forces and have the same direction, and the distance between their lines of action is 80 cm. Given that the magnitude of their resultant is 119 N, and it is 27 cm away from , find the magnitudes of the two forces, rounding your answer to two decimal places if necessary.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q13: **

The magnitude of the resultant of two parallel forces and is 192 N, where the magnitude of is 64 N, and its line of action is 57 cm away from that of the resultant’s. If the two forces have the same direction, determine the magnitude of and the distance between the lines of action of the two forces .

- A ,
- B ,
- C ,
- D ,

**Q14: **

and 26 N are two parallel forces, where is their resultant. Given that and , determine the magnitudes of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q15: **

The magnitude of the resultant of two parallel forces and is 165 N, where the magnitude of is 90 N, and its line of action is 36 cm away from that of the resultant’s. If the two forces have the same direction, determine the magnitude of and the distance between the lines of action of the two forces .

- A ,
- B ,
- C ,
- D ,

**Q16: **

Two vertical forces are acting on a horizontal light rod . The smaller force has magnitude 108 N and acts on end . The other force acts on end . Determine the length of the rod given that the magnitude of the forces’ resultant equals 84 N, and the distance between its line of action and is 18 cm.