**Q3: **

Rectangle has vertices , , , and . Use vectors to determine its area.

**Q4: **

If and , find .

- A
- B
- C
- D

**Q5: **

A book moves on a horizontal plane after being pushed by a force of 12 N parallel to the plane. The friction force between the book and the plane is 5 N. Find the resultant of these forces, and express it in terms of , the unit vector in the direction of the bookβs motion.

- A N
- B N
- C N
- D N

**Q6: **

The forces , , and act on a particle, where and are two perpendicular unit vectors. Given that the forcesβ resultant , determine the values of and .

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

**Q7: **

The resultant of forces , , and , makes an angle with the positive -axis. Determine , the magnitude of the resultant, and the value of .

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

**Q8: **

Given that , , and their resultant , determine the values of and .

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

**Q9: **

All the sides of rhombus are of length 5. Suppose that and that . Use vector multiplication to find the lengths of the two diagonals.

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

**Q10: **

is a square, in which the coordinates of the points , , and are , , and . Use vectors to determine the coordinates of the point and the area of the square.

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

**Q11: **

Given that and , determine the area of the parallelogram whose adjacent sides are represented by and .

**Q12: **

Trapezium has vertices , , , and . Given that and , find the area of that trapezium.

**Q13: **

Given a trapezium , in which and , find the value of such that .

- A
- B8
- C
- D

**Q14: **

is a rectangle, in which the coordinates of the points , , and are , , and , respectively. Use vectors to find the value of and the coordinates of point .

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

**Q15: **

Given the information in the diagram below, find the value of such that .

- A
- B
- C
- D

**Q16: **

Given a triangle , in which , , and , use vectors to determine the length of .

- A cm
- B cm
- C cm
- D cm

**Q17: **

In the given figure, and are parallel lines; however, is NOT parallel to either or . Given that , , and , determine whether and are in the same, opposite, or different directions.

- Adifferent
- Bsame
- Copposite