# Worksheet: Cross Product in 2D

In this worksheet, we will practice finding the cross product of two vectors in the coordinate plane.

**Q1: **

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,

**Q2: **

A rectangle has vertices , , , and . Use vectors to determine its area.

**Q4: **

If and , find .

**Q5: **

is a square of side 4, and is a unit vector perpendicular to the squareβs plane. Find .

**Q6: **

In the rectangle shown in the figure, calculate if form a right-hand system of unit vectors.

- A
- B
- C
- D

**Q7: **

If , , , and , find .

- A
- B
- C
- D

**Q8: **

Given that , , and , determine .

- A
- B
- C
- D

**Q9: **

If , , , and , find .

- A
- B
- C
- D

**Q11: **

Given that is a square with side length 27 cm, and is the unit vector perpendicular to its plane, determine .

- A
- B
- C
- D

**Q12: **

Given that is a square with side 49, and is the unit vector perpendicular to its plane, determine .

- A
- B
- C
- D

**Q13: **

If is a square with a side length of 81 cm, and is a unit vector perpendicular to its plane, find .

- A
- B
- C
- D

**Q14: **

is a rectangle where is a unit vector perpendicular to its plane. Find .

- A
- B
- C
- D

**Q15: **

is a rectangle where is a unit vector perpendicular to its plane. Find .

- A
- B
- C
- D

**Q16: **

Given that , and , and , find the value of .

- A
- B
- C
- D
- E

**Q17: **

Find the value of .

- A
- B2
- C1
- D
- E0

**Q18: **

Find the area of a triangle , where , , and .

**Q19: **

is a rhombus, in which the coordinates of the points and are and , respectively. Use vectors to determine its perimeter.

- A length units
- B length units
- C length units
- D666 length units

**Q20: **

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